DMRG DMRG cond-mat Papers

Condensed matter physics papers from the DMRG research group with abstracts and LaTeX rendering

Generated on 2026-01-01 01:23:01

Total papers: 1259

Recent Papers

Non-compact 3D TQFT and non-semisimplicity

Authors: Theodoros Lagiotis

arXiv ID: 2512.23698 | Date: 2025-12-29

Abstract: We define a once extended non-compact 3-dimensional TQFT Z\mathcal{Z} from the data of a (potentially) non-semisimple modular tensor category. This is in the framework of generators and relations of [Bartlett et al., arxiv:1509.06811 (2015)], having disallowed generating 2-morphisms whose source is the empty. Moreover, we show that the projective mapping class group representations this TQFT gives rise to, are dual to those of [Lyubashenko, arXiv:hep-th/9405167 (1994)] and [De Renzi et al., arXiv:2010.14852 (2020)]. We develop a method to decompose a closed 3-manifold in terms of 2-morphism generators. We use this to compute the value of Z\mathcal{Z} on 3-manifolds, explaining why it should recover Lyubashenko's 3-manifold invariants [Lyubashenko, arXiv:hep-th/9405167 (1994)]. Finally, we explain that the value of the non-compact TQFT on the solid torus recovers the data of a modified trace [Geer et al., arXiv:0711.4229 (2007)].

Fractional quantum anomalous Hall and anyon density-wave halo in a minimal interacting lattice model of twisted bilayer MoTe2_2

Authors: Chuyi Tuo, Ming-Rui Li, Hong Yao

arXiv ID: 2512.23608 | Date: 2025-12-29

Abstract: The experimental discovery of fractional quantum anomalous Hall (FQAH) states in tunable moiré superlattices has sparked intense interest in exploring the interplay between topological order and symmetry breaking phases. In this paper, we present a comprehensive numerical study of this interplay through large-scale density matrix renormalization group (DMRG) simulations on a minimal two-band lattice model of twisted bilayer MoTe2_2 at filling ν=2/3ν=-2/3. We find robust FQAH ground states and provide clear numerical evidences for anyon excitations with fractional charge and pronounced real-space density modulations, directly supporting the recently proposed anyon density-wave halo picture. We also map out the displacement field dependent phase diagram, uncovering a rich landscape of charge ordered states emerging from the FQAH, including a quantum anomalous Hall crystal (QAHC) with an integer quantized Hall conductance. We expect our work to inspire further research interest of intertwined correlated topological phases in moiré systems.

Multi-orbital dynamical mean-field theory with a complex-time solver

Authors: Yang Yu, Lei Zhang, Emanuel Gull, Xiaodong Cao, Xinyang Dong

arXiv ID: 2512.23237 | Date: 2025-12-29

Abstract: We present the combination of a complex-time tensor-network impurity solver with an analytic continuation scheme based on exponential fitting as an efficient framework for single and multi-orbital dynamical mean-field calculations. By performing time-evolution along a complex-time contour, the approach balances computational cost with the difficulty of spectral recovery, offering greater flexibility than methods confined to the real or imaginary axis. By complementing the complex-time evolution with an exponential fitting scheme, we faithfully extract real-time information at negligible cost. The resulting method obtains high-resolution spectra at a significantly lower computational cost than real-time evolution, offering a promising tool for ab initio studies of strongly correlated materials.

Efficient population transfer in a quantum dot exciton under phonon-induced decoherence via shortcuts to adiabaticity

Authors: Spyridon G. Kosionis, Sutirtha Biswas, Christina Fouseki, Dionisis Stefanatos, Emmanuel Paspalakis

arXiv ID: 2512.23016 | Date: 2025-12-28

Abstract: In the present study, we apply shortcut to adiabaticity pulses (time-dependent Rabi frequency and detuning) for the efficient population transfer from the ground to the exciton state in a GaAs/InGaAs quantum dot with phonon-induced dephasing. We use the time-evolving matrix product operator (TEMPO) method to propagate system in time and find that, for temperatures below 20 K20 \ \text{K} and pulse duration up to 10 ps10 \ \text{ps}, a very good transfer efficiency is obtained in general. We explain these results using a Bloch-like equation derived from a generalized Lindblad equation, which adequately describes system dynamics at lower temperatures. For higher temperatures, the transfer efficiency is significantly reduced except for subpicosecond pulses, where the shortcut Rabi frequency reduces to a delta pulse attaining a fast population inversion. The present work is expected to find application in quantum technologies which exploit quantum dots for single-photon generation on demand.

Graph restricted tensors: building blocks for holographic networks

Authors: Rafaĺ Bistroń, Márton Mestyán, Balázs Pozsgay, Karol Życzkowski

arXiv ID: 2512.23005 | Date: 2025-12-28

Abstract: We analyze few-body quantum states with particular correlation properties imposed by the requirement of maximal bipartite entanglement for selected partitions of the system into two complementary parts. A novel framework to treat this problem by encoding these constraints in a graph is advocated; the resulting objects are called ``graph-restricted tensors''. This framework encompasses several examples previously treated in the literature, such as 1-uniform multipartite states, quantum states related to dual unitary operators and absolutely maximally entangled states (AME) corresponding to 2-unitary matrices. Original examples of presented graph-restricted tensors are motivated by tensor network models for the holographic principle. In concrete cases we find exact analytic solutions, demonstrating thereby that there exists a vast landscape of non-stabilizer tensors useful for the lattice models of holography.

Kitaev interaction and possible spin liquid state in CoI2 and Co2/3Mg1/3I2

Authors: Yaozhenghang Ma, Ke Yang, Yuxuan Zhou, Hua Wu

arXiv ID: 2512.22453 | Date: 2025-12-27

Abstract: Kitaev materials are of great interest due to their potential in realizing quantum spin liquid (QSL) states and applications in topological quantum computing. In the pursuit of realizing Kitaev QSL, a Mott insulator with strong bond-dependent frustration and weak geometric frustration is highly desirable. Here we explore Kitaev physics in the van der Waals triangular antiferromagnet (AF) CoI2_2, through the spin-orbital states and Wannier function analyses, exact diagonalization and density matrix renormalization group study of the electronic structure and magnetic properties. We find that the high-spin Co2+^{2+} ion is in the Jeff=1/2J_\mathrm{eff}=1/2 state because of strong spin-orbit coupling, and the weak trigonal elongation and crystal field contribute to the observed weak in-plane magnetic anisotropy. The strong t2gt_{2g}-ege_g hopping via the strong Co 3dd-I 5pp hybridization gives rise to a strong Kitaev interaction (K1K_1) at the first nearest neighbors (1NN), and the long Co-Co distance and the weak t2gt_{2g}-t2gt_{2g} hoppings determine a weak Heisenberg interaction J1J_1. The resultant K1/J1|K_1/J_1| = 6.63 confirms a strong bond-dependent frustration, while the geometric frustration due to the 3NN Heisenberg interaction J3J_3 gets involved, and they all together result in the experimental helical AF order in CoI2_2. We then propose to suppress the J3J_3 using a partial Mg substitution for Co, and indeed we find that Co2/3_{2/3}Mg1/3_{1/3}I2_2 has the much reduced geometric frustration but hosts the robust bond-dependent frustration, and thus it would be a promising Kitaev material being so far closest to the QSL state.

Site-Order Optimization in the Density Matrix Renormalization Group via Multi-Site Rearrangement

Authors: Ryo Watanabe, Toshiya Hikihara, Hiroshi Ueda

arXiv ID: 2512.22021 | Date: 2025-12-26

Abstract: In the approaches based on matrix-product states (MPSs), such as the density-matrix renormalization group (DMRG) method, the ordering of the sites crucially affects the computational accuracy. We investigate the performance of an algorithm that searches for the optimal site order by iterative local site rearrangement. We improve the algorithm by expanding the range of site rearrangement and apply it to a one-dimensional quantum Heisenberg model with random site permutation. The results indicate that increasing the range of the site rearrangement significantly improves the computational accuracy of the DMRG method. In particular, increasing the rearrangement range from two to three sites reduces the average relative error in the ground-state energy by 65% to 94% in the cases we tested. We also discuss the computational cost of the algorithm and its application as a preprocessing for MPS-based calculations.

Simulating triangle Hofstadter-Hubbard model with fermionic projected entangled simplex states

Authors: Sen Niu, D. N. Sheng, Yang Peng

arXiv ID: 2512.21503 | Date: 2025-12-25

Abstract: The triangular Hofstadter-Hubbard model, realizable in moiré bilayers, provides a fertile ground for discovering correlated topological states. We investigate this model in the grand canonical ensemble by introducing a fermionic infinite projected entangled simplex state (iPESS) approach, which offers direct access to the stability of the emergent correlated states at the thermodynamic limit. Through numerically optimizing fermionic iPESS, we accurately capture the chiral spin liquid (CSL) phase in the Mott insulating regime, characterized by a uniform chiral order, entanglement spectrum and the appearance of gossamer correlation tails in spin channel. The intermediate-UU CSL is separated from the weak-UU Chern insulator by a Mott transition at Uc111.5U_{c_1} \approx 11.5, signaled by changes in the charge fluctuation and compressibility. Finite-correlation-length scaling of the magnetization reveals a transition into a large-UU 120120^\circ Néel phase at Uc222.5U_{c_2} \approx 22.5. Remarkably, with finite hole doping δδ, we identify a uniform superconducting state with a finite pairing amplitude, whose order parameter displays a nearly universal phase winding across the UU-δδ phase diagram. Our work demonstrates robust chiral superconductivity in the thermodynamic limit through doping Chern insulator and CSL.

Universality of equilibration dynamics after quantum quenches

Authors: Vincenzo Alba, Sanam Azarnia, Gianluca Lagnese, Federico Rottoli

arXiv ID: 2512.21313 | Date: 2025-12-24

Abstract: We investigate the distribution of the eigenvalues of the reduced density matrix (entanglement spectrum) after a global quantum quench. We show that in an appropriate scaling limit the lower part of the entanglement spectrum exhibits ``universality''. In the scaling limit and at asymptotically long times the distribution of the entanglement spectrum depends on two parameters that can be determined from the Rényi entropies. We show that two typical scenarios occur. In the first one, the distribution of the entanglement spectrum levels is similar to the one describing the ground-state entanglement spectrum in Conformal Field Theories. In the second scenario, the lower levels of the entanglement spectrum are highly degenerate and their distribution is given by a series of Dirac deltas. We benchmark our analytical results in free-fermion chains, such as the transverse field Ising chain and the XX chain, in the rule 54 chain, and in Bethe ansatz solvable spin models.

Black hole as a multipartite entangler: multi-entropy in AdS3{}_3/CFT2{}_2

Authors: Takanori Anegawa, Shota Suzuki, Kotaro Tamaoka

arXiv ID: 2512.21037 | Date: 2025-12-24

Abstract: We study multipartite entanglement in typical pure states holographically dual to pure BTZ black holes, using multi-entropy and its ``genuine'' version. In the bulk, these quantities are computed by minimal geodesic networks (so-called Steiner trees). We find that at sufficiently high temperature, the genuine tripartite multi-entropy exhibits a volume-law scaling in sharp contrast to vacuum AdS3_3, where the genuine contribution is universal and size-independent. Moreover, we find another phase: once one subsystem exceeds half of the total system, the leading genuine tripartite entanglement vanishes and reduces to that for global AdS3{}_3. This transition is indeed consistent with recent arguments for distillable EPR pairs in tripartite Haar-random states. Motivated by finite-cutoff holography, we further study the radial cutoff dependence of multi-entropy and show that genuine multi-entropy acquires nontrivial size dependence even for the tripartite case in AdS3{}_3. As a byproduct, we also observe an intriguing ``area-law'' contribution to multi-entropy that is relevant to vacuum AdS3{}_3.

Competing magnetic and topological orders in the spin-1 Kitaev-Heisenberg chain with single-ion anisotropy

Authors: Sahinur Reja, Satoshi Nishimoto

arXiv ID: 2512.20912 | Date: 2025-12-24

Abstract: We investigate the ground-state phase diagram of the spin-1 Kitaev--Heisenberg chain in the presence of uniaxial single-ion anisotropy (SIA) DzD_z by density-matrix renormalization group (DMRG) calculations. By combining energy-curvature diagnostics on periodic N=24N=24 clusters with a refined characterization based on order parameters and correlation functions for open chains up to N=144N=144, we establish a comprehensive phase diagram in the φφ--DzD_z plane. We identify four magnetically ordered phases -- FM-zz, FM-xyxy, Néel-zz, and a two-sublattice collinear LLRR2 state -- as well as magnetically disordered/critical regimes including Néel-xyxy, LLRR1, and two Kitaev spin-liquid (KSL) regions. A topological Haldane phase also emerges near the Heisenberg limit. Our results provide evidence that both AFM- and FM-KSL regimes acquire finite parameter widths in the spin-1 model, while the Haldane phase is fragile against Kitaev-type anisotropy, particularly for Dz<0D_z<0. Increasing (decreasing) DzD_z suppresses (enhances) magnetic order and expands (shrinks) the KSL and other magnetically disordered sectors. Also, at Dz=0D_z=0, we identify an exactly solvable point at φ=tan1(2)φ=\tan^{-1}(-2), which enforces a first-order transition between Néel-zz and LLRR2. We further contrast these findings with the spin-1/21/2 KH chain and with the spin-1 honeycomb KH model, highlighting the distinct roles of dimensionality and SIA in Kitaev-type magnets.

Quantum Ising Model on (2+1)(2+1)-Dimensional Anti-de Sitter Space using Tensor Networks

Authors: Simon Catterall, Alexander F. Kemper, Yannick Meurice, Abhishek Samlodia, Goksu Can Toga

arXiv ID: 2512.20838 | Date: 2025-12-23

Abstract: We study the quantum Ising model on (2+1)-dimensional anti-de Sitter space using Matrix Product States (MPS) and Matrix Product Operators (MPOs). Our spatial lattices correspond to regular tessellations of hyperbolic space with coordination number seven. We find the ground state of this model using the Density Matrix Renormalization Group (DMRG) algorithm which allowed us to probe lattices that range in size up to 232 sites. We explore the bulk phase diagram of the theory and find disordered and ordered phases separated by a phase transition. We find that the boundary-boundary spin correlation function exhibits power law scaling deep in the disordered phase of the Ising model consistent with the anti-de Sitter background. By tracing out the bulk indices, we are able to compute the density matrix for the boundary theory. At the critical point, we find the entanglement entropy exhibits the logarithmic dependence of boundary length expected for a one-dimensional CFT but away from this, we see a linear scaling. In comparison, the full system exhibits a volume law scaling, which is expected in chaotic and highly connected systems. We also measure Out-of-time-Ordered-Correlators (OTOCs) to explore the scrambling behavior of the theory.

Simulating fermionic fractional Chern insulators with infinite projected entangled-pair states

Authors: Hao Chen, Titus Neupert, Juraj Hasik

arXiv ID: 2512.20697 | Date: 2025-12-23

Abstract: Infinite projected entangled-pair states (iPEPS) provide a powerful variational framework for two-dimensional quantum matter and have been widely used to capture bosonic topological order, including chiral spin liquids. Here we extend this approach to \emph{fermionic} topological order by variationally optimizing U(1)U(1)-symmetric fermionic iPEPS for a fractional Chern insulator (FCI), with bond dimensions up to D=9D=9. We find evidence for a critical bond dimension, above which the ansatz faithfully represents the FCI phase. The FCI state is characterized using bulk observables, including the equal-time single-particle Green's function and the pair-correlation function, as well as the momentum-resolved edge entanglement spectrum. To enable entanglement-spectrum calculations for large iPEPS unit cells, we introduce a compression scheme and show that the low-lying part of the spectrum is already well converged at relatively small cutoff dimensions.

Variational (matrix) product states for combinatorial optimization

Authors: Guillermo Preisser, Conor Mc Keever, Michael Lubasch

arXiv ID: 2512.20613 | Date: 2025-12-23

Abstract: To compute approximate solutions for combinatorial optimization problems, we describe variational methods based on the product state (PS) and matrix product state (MPS) ansatzes. We perform variational energy minimization with respect to a quantum annealing Hamiltonian and utilize randomness by embedding the approaches in the metaheuristic iterated local search (ILS). The resulting quantum-inspired ILS algorithms are benchmarked on maximum cut problems of up to 50000 variables. We show that they can outperform traditional (M)PS methods, classical ILS, the quantum approximate optimization algorithm and other variational quantum-inspired solvers.

Quantum State Preparation via Schmidt Spectrum Optimisation

Authors: Josh Green, Joshua Snow, Jingbo B Wang

arXiv ID: 2512.20537 | Date: 2025-12-23

Abstract: We introduce an efficient algorithm for the systematic design of shallow-depth quantum circuits capable of preparing many-body quantum states represented as Matrix Product States (MPS). The proposed method leverages Schmidt spectrum optimization (SSO) to minimize circuit depth while preserving the entanglement structure inherent to MPS representations, thereby enabling scalable state preparation on near-term quantum hardware. The core idea is to \textit{disentangle} the target MPS using a sequence of optimised local unitaries, and then reverse this process to obtain a state preparation circuit. Specifically, we define a loss function directly on the Schmidt spectra of intermediate states and use automatic differentiation to optimise each circuit layer so as to systematically reduce entanglement entropy. Once a disentangling sequence has been learned, we take the adjoints of the optimised unitaries to obtain a shallow-depth circuit that approximately reconstructs the target MPS from the computational all-zero state. We benchmark SSO across a range of MPS approximations to the ground states of local Hamiltonians and demonstrate state-of-the-art shallow-depth performance, improving accuracy by up to an order of magnitude over existing methods. Finally, we provide numerical evidence that SSO mitigates the adverse time-complexity scaling observed in previous disentangling-based approaches.

Tensor-network study of the ground state of maple-leaf Heisenberg antiferromagnet

Authors: Samuel Nyckees, Pratyay Ghosh, Frédéric Mila

arXiv ID: 2512.20466 | Date: 2025-12-23

Abstract: We study the quantum phase diagram of the spin-1/21/2 nearest-neighbor Heisenberg model on the maple-leaf lattice using infinite projected entangled pair states (iPEPS) combined with a corner transfer matrix renormalization group scheme adapted to C3C_3-symmetric lattices. Focusing on the fully antiferromagnetic JJ-JdJ_d model with Jh=Jt:=JJ_h = J_t := J, we map out the ground-state phase diagram as a function of the dimer coupling JdJ_d. Our results show that the system hosts only two phases: a magnetically ordered canted-120120^\circ phase and an exact dimer singlet product phase. We identify a first-order transition between these two phases at Jd/J1.45J_d/J \approx 1.45. Within the magnetically ordered phase, we observe small but finite magnetic moments. We also resolve the quantum renormalization of the canting angle, which deviates from the classical prediction over almost the entire magnetically ordered phase.

Tree tensor network states represent low-energy states faithfully

Authors: Thomas Barthel

arXiv ID: 2512.20215 | Date: 2025-12-23

Abstract: Extending corresponding results for matrix product states [Verstraete and Cirac, PRB 73, 094423 (2006); Schuch et al. PRL 100, 030504 (2008)], it is shown how the approximation error of tree tensor network states (TTNS) can be bounded using Schmidt spectra or Rényi entanglement entropies of the target quantum state. Conversely, one obtains bounds on TTNS bond dimensions needed to achieve a specific approximation accuracy. For tree lattices, the result implies that efficient TTNS approximations exist if α<1α<1 Rényi entanglement entropies for single-branch cuts obey an area law, as in ground and low-energy states of certain gapped systems.

FastMPS: Revisit Data Parallel in Large-scale Matrix Product State Sampling

Authors: Yaojian Chen, Si-Qiu Gong, Lin Gan, Yanfei Liu, An Yang, Yinuo Wang, Chao-yang Lu, Guangwen Yang

arXiv ID: 2512.20064 | Date: 2025-12-23

Abstract: Matrix Product State (MPS) is a versatile tensor network representation widely applied in quantum physics, quantum chemistry, and machine learning, etc. MPS sampling serves as a critical fundamental operation in these fields. As the problems become more complex, the scale of MPS is rapidly increasing. Traditional data parallelism is limited by memory and heavy I/O in large-scale MPS. Model parallelism that can handle large-scale MPS imposes rigid process bindings and lacks scalability. This work proposes Fast-MPS, a multi-level parallel framework for scalable MPS sampling. Our design combines data parallelism across samples with tensor parallelism along bond dimensions. We eliminate memory and I/O pressure through compression and overlapping, and revive data parallel in large-scale MPS sampling. We evaluate our approach on Gaussian Boson Sampling, a representative and demanding application. Fast-MPS achieves over 10x speedup compared to existing simulators, scales to thousands of processes, and enables simulations with 8,176 sites and bond dimension chi = 10^4, significantly outperforming the state of the art. Fast-MPS has demonstrated great potential in high-performance tensor network applications.

Controlled pairing symmetries in a Fermi-Hubbard ladder with band flattening

Authors: J. P. Mendonça, S. Biswas, M. Dziurawiec, U. Bhattacharya, K. Jachymski, M. Aidelsburger, M. Lewenstein, M. M. Maśka, T. Grass

arXiv ID: 2512.20689 | Date: 2025-12-22

Abstract: Band flattening has been identified as key ingredient to correlation phenomena in Moiré materials and beyond. Here, we examine strongly repulsive fermions on a ladder -- a minimal platform for unconventional dd-wave pairing -- and show that flattening of the lower band through an additional diagonal hopping term produces non-Fermi liquid behavior, evidenced by the violation of Luttinger's theorem, as well as axial dd-wave pairing correlations. Alternatively, plaquette ring exchange can also generate pairing, albeit with a distinct diagonal dd-wave pairing symmetry. Hence, our finding showcases a competition of different unconventional pairing channels, and demonstrates via a simple model how band geometry can induce fermionic pairing. This offers broadly relevant insights for correlated flat-band systems, ranging from ultracold atoms to strongly interacting electrons in solids.

Ergotropy of quantum many-body scars

Authors: Zhaohui Zhi, Qingyun Qian, Jin-Guo Liu, Guo-Yi Zhu

arXiv ID: 2512.19801 | Date: 2025-12-22

Abstract: Quantum many-body scars break ergodicity and evade thermalization, resulting in area law entanglement entropy even with high energy density. While their quantum correlations and entanglement have been elaborated previously, their capacity in storing extractable energy, quantified by the notion ergotropy, remains an open question. Here we focus on the representative PXP model, and unveil the extensive ergotropy scaling of a family of states interpolating between quantum many-body scars and thermal states, the latter of which are known to be passive with vanishing ergotropy. A phenomenological relation between ergotropy and entanglement is uncovered, which generalizes the existing free fermion integrable results to an interacting scenario. The ergotropy in a dynamical protocol shows that a reset with a global uniform coherent rotation can inject extractable energy, as a proof of principle way to charge a quantum "battery". Our protocol is tailored for near term Rydberg neutral atoms array, while also being feasible for other quantum processors. Our results establish that quantum many-body scars, despite the tiny fraction of the Hilbert space they occupy, can be efficiently exploited for storing extractable energy, and "scarring" a many-body system as a promising route for engineering quantum many-body battery.

Learning transitions of topological surface codes

Authors: Finn Eckstein, Bo Han, Simon Trebst, Guo-Yi Zhu

arXiv ID: 2512.19786 | Date: 2025-12-22

Abstract: For the surface code, topological quantum order allows one to encode logical quantum information in a robust, long-range entangled many-body quantum state. However, if an observer probes this quantum state by performing measurements on the underlying qubits, thereby collecting an ensemble of highly correlated classical snapshots, two closely related questions arise: (i) do measurements decohere the topological order of the quantum state; and (ii) how much of the logical information can one learn from the snapshots? Here we address these questions for measurements in a uniform basis on all qubits. We find that for generic measurement angles, sufficiently far away from the Clifford X, Y, and Z directions (such as the X+Y+Z basis) the logical information is never lost in one of the following two ways: (i) for weak measurement, the topological order is absolutely robust; (ii) for projective measurement, the quantum state inevitably collapses, but the logical quantum information is faithfully transferred from the quantum system to the observer in the form of a tomographically complete classical shadow. At these generic measurement angles and in the projective-measurement limit, the measurement ensemble enforced by Born probabilities can be represented by a 2D tensor network that can be fermionized into a disordered, free-fermion network model in symmetry class DIII, which gives rise to a Majorana "metal" phase. When the measurement angle is biased towards the X or Z limits, a critical angle indicates the threshold of a learning transition beyond which the classical shadow no longer reveals full tomographic information (but reduces to a measurement of the logical X or Z state). This learning transition can be described in the language of the network model as a "metal to insulator" transition...

Thermodynamics of large-scale chemical reaction networks

Authors: Schuyler B. Nicholson, Luis Pedro García-Pintos

arXiv ID: 2512.19616 | Date: 2025-12-22

Abstract: Chemical and biological networks can describe a wide variety of processes, from gene regulatory networks to biochemical oscillations. Modeled by chemical master equations, these processes are inherently stochastic, as fluctuations dominate deterministic order at mesoscopic scales. These classic many-body processes suffer from the so-called curse of high dimensionality, which makes exact mathematical descriptions exponentially expensive to compute. The exponential cost renders the study of the thermodynamic properties of such systems out of equilibrium intractable and forces approximations of system noise or assumptions of continuous particle numbers. Here, we use tensor networks to numerically explore the thermodynamics of chemical processes by directly solving the ensemble solution of the chemical master equation with efficient (sub-exponential) computational cost. We provide accurate estimates of the entropy production rate, heat flux, chemical work, and nonequilibrium thermodynamic potentials, free from sampling errors or mean-field approximations. We illustrate our results through a dissipative self-assembly model. In this way, we show how tensor networks can inform the design of efficient chemical processes in previously unattainable regimes.

Input phase noise in Gaussian Boson sampling

Authors: Magdalena Parýzková, Craig S. Hamilton, Igor Jex, Michael Stefszky, Christine Silberhorn

arXiv ID: 2512.19596 | Date: 2025-12-22

Abstract: Gaussian boson sampling is an important protocol for testing the performance of photonic quantum simulators. As such, various noise sources have been investigated that degrade the operation of such devices. In this paper, we examine a situation with phase noise between different modes of the input state leading to dephasing of the system. This models the phase fluctuations which remain even when the mean phase is controlled. We aim to determine whether these phase-noisy input states still form a computationally difficult problem. To do this, we use Matrix Product Operators to model the system, a technique recently used to model boson sampling scenarios. Our investigation finds that the Entanglement entropy grows linearly with the number of input states even for noisy input states. This implies that, unlike boson loss, this form of experimentally relevant noise remains difficult to simulate with tensor networks and may allow for the demonstration of quantum advantage without the need for implementing the challenging task of input-state phase stabilisation.

Extracting quantum field theory dynamics from an approximate ground state

Authors: Sophie Mutzel, Antoine Tilloy

arXiv ID: 2512.19594 | Date: 2025-12-22

Abstract: We develop a linear-programming method to extract dynamical information from static ground-state correlators in quantum field theory. We recast the Källén-Lehmann inversion as a convex optimization problem, in a spirit similar to the recent approach of Lawrence [arXiv:2408.11766]. This produces robust estimates of the smeared spectral density, the real-time propagator, and the mass gap directly from an approximate equal-time two-point function, and simultaneously yields an \emph{a posteriori} lower bound on the correlation-function error. We test the method on the 1+11+1-dimensional φ4φ^4 model, using a variational approximation to the vacuum -- relativistic continuous matrix product states -- that provides accurate correlators in the continuum and thermodynamic limits. The resulting mass gaps agree with renormalized Hamiltonian truncation and Borel-resummed perturbation theory across a wide range of couplings, demonstrating that accurate dynamical data can be recovered from a single equal-time slice.

Boundary Criticality at the Nishimori Multicritical Point

Authors: Sheng Yang, Xinyu Sun, Shao-Kai Jian

arXiv ID: 2512.19523 | Date: 2025-12-22

Abstract: We study boundary critical behavior at the Nishimori multicritical point of the two-dimensional (2D) random-bond Ising model. Using tensor-network methods, we realize a one-parameter family of microscopic boundary conditions by continuously rotating the boundary-spin orientation and find two conformal boundary fixed points that correspond to the free and fixed boundaries. We extract conformal data, including the boundary entropies and the scaling dimensions of boundary primary operators, which characterize the boundary universality class. We further demonstrate that the free boundary fixed point exhibits multifractal scaling of boundary spin fields. Finally, we complement our numerical results with a renormalization group analysis and discuss a systematic bridge between the controlled 6ε6-ε expansion and the 2D tensor network numerics.

Holographic Tensor Networks as Tessellations of Geometry

Authors: Qiang Wen, Mingshuai Xu, Haocheng Zhong

arXiv ID: 2512.19452 | Date: 2025-12-22

Abstract: Holographic tensor networks serve as toy models for the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence, capturing many of its essential features in a concrete manner. However, existing holographic tensor network models remain far from a complete theory of quantum gravity. A key obstacle is their discrete structure, which only approximates the semi-classical geometry of gravity in a qualitative sense. In \cite{Lin:2024dho}, it was shown that a network of partial-entanglement-entropy (PEE) threads, which are bulk geodesics with a specific density distribution, generates a perfect tessellation of AdS space. Moreover, such PEE-network tessellations can be constructed for more general geometries using the Crofton formula. In this paper, we assign a quantum state to each vertex in the PEE network and develop two holographic tensor network models: the factorized PEE tensor network, which takes the form of a tensor product of EPR pairs, and the random PEE tensor network. In both models we reproduce the exact Ryu-Takayanagi formula by showing that the minimal number of cuts along a homologous surface in the network exactly computes the area of this surface.

Tree tensor networks for many-body localization in two dimensions

Authors: Lars Humpert, Dante M. Kennes, Jan-Niklas Herre

arXiv ID: 2512.19389 | Date: 2025-12-22

Abstract: We investigate the disordered spin-12\frac12Heisenberg model in two dimensions and employ tree tensor networks (TTNs) with a physics-informed structural optimization of the tree layout, to simulate dynamics in the many-body localization problem. We find that TTNs are able to capture two-dimensional entanglement patterns more effectively than matrix product states (MPS) while being more efficient to contract than projected entangled pair states (PEPS) to probe larger systems and longer times. Structural optimization of the trees based on time evolution of the entanglement in the system allows to keep the necessary bond dimensions low and to maximally exploit the increased expressiveness of TTNs over MPS. In this way, we achieve more accurate results in all considered parameter regimes both below and above the ergodicity-to-localization crossover at a comparable compute-time cost.

DeepQuantum: A PyTorch-based Software Platform for Quantum Machine Learning and Photonic Quantum Computing

Authors: Jun-Jie He, Ke-Ming Hu, Yu-Ze Zhu, Guan-Ju Yan, Shu-Yi Liang, Xiang Zhao, Ding Wang, Fei-Xiang Guo, Ze-Feng Lan, Xiao-Wen Shang, Zi-Ming Yin, Xin-Yang Jiang, Lin Yang, Hao Tang, Xian-Min Jin

arXiv ID: 2512.18995 | Date: 2025-12-22

Abstract: We introduce DeepQuantum, an open-source, PyTorch-based software platform for quantum machine learning and photonic quantum computing. This AI-enhanced framework enables efficient design and execution of hybrid quantum-classical models and variational quantum algorithms on both CPUs and GPUs. For photonic quantum computing, DeepQuantum implements Fock, Gaussian, and Bosonic backends, catering to different simulation needs. Notably, it is the first framework to realize closed-loop integration of three paradigms of quantum computing, namely quantum circuits, photonic quantum circuits, and measurement-based quantum computing, thereby enabling robust support for both specialized and universal photonic quantum algorithm design. Furthermore, DeepQuantum supports large-scale simulations based on tensor network techniques and a distributed parallel computing architecture. We demonstrate these capabilities through comprehensive benchmarks and illustrative examples. With its unique features, DeepQuantum is intended to be a powerful platform for both AI for Quantum and Quantum for AI.

El Agente Cuántico: Automating quantum simulations

Authors: Ignacio Gustin, Luis Mantilla Calderón, Juan B. Pérez-Sánchez, Jérôme F. Gonthier, Yuma Nakamura, Karthik Panicker, Manav Ramprasad, Zijian Zhang, Yunheng Zou, Varinia Bernales, Alán Aspuru-Guzik

arXiv ID: 2512.18847 | Date: 2025-12-21

Abstract: Quantum simulation is central to understanding and designing quantum systems across physics and chemistry. Yet it has barriers to access from both computational complexity and computational perspectives, due to the exponential growth of Hilbert space and the complexity of modern software tools. Here we introduce{\cinzel El Agente Cuántico}, a multi-agent AI system that automates quantum-simulation workflows by translating natural-language scientific intent into executed and validated computations across heterogeneous quantum-software frameworks. By reasoning directly over library documentation and APIs, our agentic system dynamically assembles end-to-end simulations spanning state preparation, closed- and open-system dynamics, tensor-network methods, quantum control, quantum error correction, and quantum resource estimation. The developed system unifies traditionally distinct simulation paradigms behind a single natural-language interface. Beyond reducing technical barriers, this approach opens a path toward scalable, adaptive, and increasingly autonomous quantum simulation, enabling faster exploration of physical models, rapid hypothesis testing, and closer integration between theory, simulation, and emerging quantum hardware.

Dynamical Spectral Function of the Kagome Quantum Spin Liquid

Authors: Jiahang Hu, Runze Chi, Yibin Guo, B. Normand, Hai-Jun Liao, T. Xiang

arXiv ID: 2512.18831 | Date: 2025-12-21

Abstract: Quantum spin liquids (QSLs) host exotic fractionalized magnetic and gauge-field excitations whose microscopic origins and experimental verification remain frustratingly elusive. In the absence of static magnetic order, the spin excitation spectrum constitutes the crucial probe of QSL behavior, but its theoretical computation remains a serious challenge. Here we employ state-of-the-art tensor-network methods to obtain the full dynamical spectral function of the J1J_1-J2J_2 kagome Heisenberg model and benchmark our results by tracking their evolution across the magnetically ordered and QSL phases. Reducing J2/J1|J_2|/J_1 causes increasingly strong spin-wave renormalization, flattening these modes then merging them into a continuum characteristic of deconfined spinons at all finite energies in the QSL. The low-energy continuum and the occurrence of gap closure at multiple high-symmetry points identify this gapless QSL as the U(1) Dirac spin liquid. These results establish a unified understanding of spin excitations in highly frustrated quantum magnets and provide clear spectral fingerprints for experimental detection in candidate kagome QSL materials.

Identification and Optimization of Accurate Spin Models for Open-Shell Carbon Ladders with Matrix Product States

Authors: Andoni Agirre, Thomas Frederiksen, Geza Giedke, Tobias Grass

arXiv ID: 2512.18695 | Date: 2025-12-21

Abstract: Open-shell nanographenes offer a controlled setting to study correlated magnetism emerging from ππ-electron systems. We analyze oligo(indenoindene) molecules, non-bipartite carbon ladders whose tight-binding spectra feature a gapped, weakly dispersing manifold of quasi-zero modes, and show that their low-energy properties can be effectively mapped onto an interacting set of spin-1/2 degrees of freedom. Using Density Matrix Renormalization Group simulations of the full Fermi-Hubbard model, we obtain their excitation spectra, entanglement profiles, and spin-spin correlations. We then construct optimized delocalized fermionic modes that act as emergent spins and show that their interactions are well described by a frustrated J1J_1-J2J_2 Heisenberg chain. This effective description clarifies how spin degrees of freedom arise and interact in non-bipartite nanographene ladders, providing a compact and accurate representation of their correlated behavior.

A Hidden Quantum Markov model framework for Entanglement and Topological Order in the AKLT Chain

Authors: Abdessatar Souissi, Amenallah Andolsi

arXiv ID: 2512.18642 | Date: 2025-12-21

Abstract: This paper introduces a hidden quantum Markov models (HQMMs) framework to the Affleck-Kennedy-Lieb-Tasaki (AKLT) state-a cornerstone example of a symmetry-protected topological (SPT) phase. The model's observation system is the physical spin-1 chain, which emerges from a hidden spin-1/2 layer through well-defined quantum emission operation. We show that the underlying Markov dynamics caputure maximal entanglement through the use of significant channels relevant to the AKLT state. We also show that SPT order induces a covariance on the observation decoding channels. This establishes an additional bridge between the quantum Machine learning and many-body physics, with promising implication in topological order and quantum information.

Topological edge states in two-dimensional Z4\mathbb{Z}_4 Potts paramagnet protected by the Z4×3\mathbb{Z}_4^{\times 3} symmetry

Authors: Hrant Topchyan, Tigran Hakobyan, Mkhitar Mirumyan, Tigran A. Sedrakyan, Ara Sedrakyan

arXiv ID: 2512.18460 | Date: 2025-12-20

Abstract: We construct a two-dimensional bosonic symmetry-protected topological (SPT) paramagnet protected by an on-site G=Z4×3G=\mathbb{Z}_4^{\times 3} symmetry, starting from a three-component Z4\mathbb{Z}_4 Potts paramagnet on a triangular lattice. Within the group-cohomology framework, H3(G,U(1))Z4×7H^{3}(G,U(1))\cong \mathbb{Z}_4^{\times 7}, we focus on a "colorless" cocycle representative obtained by antisymmetrizing the basic Z4\mathbb{Z}_4 three-cocycle, and generate the corresponding SPT Hamiltonian via a cocycle-induced nonlocal unitary transformation followed by symmetry averaging. For open geometry, we derive the boundary theory explicitly: one color sector decouples, while the nontrivial edge reduces to an interacting Z4\mathbb{Z}_4 chain with next-to-nearest-neighbor constraints that admits a compact dressed-Potts form. Using DMRG we show that the boundary model is gapless, with the lowest gap scaling as 1/L1/L and an entanglement-entropy scaling consistent with a conformal field theory of central charge c=2.191(4)11/5c=2.191(4)\simeq 11/5. The rational value c=11/5c=11/5 matches the coset SU(3)3/SU(2)3SU(3)_3/SU(2)_3, making it a candidate for the continuum description of the Z4×3\mathbb{Z}_4^{\times 3} edge; we outline spectral and symmetry-resolved diagnostics needed to test this identification at the level of conformal towers beyond the central charge.

Momentum-resolved spectral functions of super-moiré systems using tensor networks

Authors: Anouar Moustaj, Yitao Sun, Tiago V. C. Antão, Jose L. Lado

arXiv ID: 2512.18397 | Date: 2025-12-20

Abstract: Computing spectral functions in large, non-periodic super-moiré systems remains an open problem due to the exceptionally large system size that must be considered. Here, we establish a tensor network methodology that allows computing momentum-resolved spectral functions of non-interacting and interacting super-moiré systems at an atomistic level. Our methodology relies on encoding an exponentially large tight-binding problem as an auxiliary quantum many-body problem, solved with a many-body kernel polynomial tensor network algorithm combined with a quantum Fourier transform tensor network. We demonstrate the method for one and two-dimensional super-moiré systems, including super-moiré with non-uniform strain, interactions treated at the mean-field level, and quasicrystalline super-moiré patterns. Furthermore, we demonstrate that our methodology allows us to compute momentum-resolved spectral functions restricted to selected regions of a super-moiré, enabling direct imaging of position-dependent electronic structure and minigaps in super-moiré systems with non-uniform strain. Our results establish a powerful methodology to compute momentum-resolved spectral functions in exceptionally large super-moiré systems, providing a tool to directly model scanning twisting microscope tunneling experiments in twisted van der Waals heterostructures.

Quantum simulation of deep inelastic scattering in the Schwinger model

Authors: Kazuki Ikeda, Zhong-Bo Kang, Dmitri E. Kharzeev, Wenyang Qian

arXiv ID: 2512.18062 | Date: 2025-12-19

Abstract: Hadronic tensors encode the nonperturbative structure of hadrons probed in deep inelastic scattering (DIS), yet their direct evaluation requires real-time evolution that presents a challenge for traditional Euclidean lattice approaches. In this work, we present the first study of the hadronic tensors in DIS using quantum simulation in the Schwinger model, i.e (1+1)-dimensional QED. Using two complementary quantum-simulation strategies -- quantum-circuit and tensor-network methods -- we compute the real-time current-current correlator directly on the lattice and validate our results against exact diagonalization where applicable. From this correlator, we compute the hadronic tensor and determine the longitudinal structure function, the sole nonvanishing DIS observable in two space-time dimensions. Our study demonstrates that quantum simulation offers a viable complementary pathway towards the evaluation of real-time observables relevant for hadronic structure. It also provides a foundation for extending the calculations from Schwinger model to other gauge theories.

Approximation and learning with compositional tensor trains

Authors: Martin Eigel, Charles Miranda, Anthony Nouy, David Sommer

arXiv ID: 2512.18059 | Date: 2025-12-19

Abstract: We introduce compositional tensor trains (CTTs) for the approximation of multivariate functions, a class of models obtained by composing low-rank functions in the tensor-train format. This format can encode standard approximation tools, such as (sparse) polynomials, deep neural networks (DNNs) with fixed width, or tensor networks with arbitrary permutation of the inputs, or more general affine coordinate transformations, with similar complexities. This format can be viewed as a DNN with width exponential in the input dimension and structured weights matrices. Compared to DNNs, this format enables controlled compression at the layer level using efficient tensor algebra. On the optimization side, we derive a layerwise algorithm inspired by natural gradient descent, allowing to exploit efficient low-rank tensor algebra. This relies on low-rank estimations of Gram matrices, and tensor structured random sketching. Viewing the format as a discrete dynamical system, we also derive an optimization algorithm inspired by numerical methods in optimal control. Numerical experiments on regression tasks demonstrate the expressivity of the new format and the relevance of the proposed optimization algorithms. Overall, CTTs combine the expressivity of compositional models with the algorithmic efficiency of tensor algebra, offering a scalable alternative to standard deep neural networks.

Charge fluctuations and topological phases in Kitaev-Heisenberg ladders

Authors: M. G. Sousa, O. Ávalos-Ovando, E. Vernek, S. E. Ulloa

arXiv ID: 2512.17596 | Date: 2025-12-19

Abstract: We investigate the stability of topological phases in doped Kitaev-Heisenberg ladders by studying the competition with itinerant electrons and the associated charge fluctuations in a Hubbard model on a honeycomb ribbon geometry. We analyze the evolution of string order parameters, spin correlations, and charge fluctuations as functions of hopping amplitude and interaction strength in a half-filled band. Our results from density matrix renormalization group (DMRG) calculations show that increasing electron bandwidth progressively suppresses the topological phases, shifting and narrowing their stability regions in the phase diagram. We identify the critical values of hopping where string order vanishes and characterize the interplay between magnetic order and charge fluctuations. These findings provide insight into the robustness of topological phases against doping and charge dynamics, with implications for candidate Kitaev materials and engineered quantum systems.

Evaluating Sample-Based Krylov Quantum Diagonalization for Heisenberg Models with Applications to Materials Science

Authors: Roman Firt, Neel Misciasci, Jonathan E. Mueller, Triet Friedhoff, Chinonso Onah, Aaron Schulze, Sarah Mostame

arXiv ID: 2512.17141 | Date: 2025-12-19

Abstract: We evaluate the Sample-based Krylov Quantum Diagonalization (SKQD) algorithm on one- and two-dimensional Heisenberg models, including strongly correlated regimes in which the ground state is dense. Using problem-informed initial states and magnetization-sector sweeps, SKQD accurately reproduces ground-state energies and field-dependent magnetization across a range of anisotropies. Benchmarks against DMRG and exact diagonalization show consistent qualitative agreement, with accuracy improving systematically in more anisotropic regimes. We further demonstrate SKQD on quantum hardware by implementing 18- and 30-qubit Heisenberg chains, obtaining magnetization curves that match theoretical expectations. Simulations on small 2D square-lattice systems further demonstrate that the method applies effectively beyond 1D geometries.

How to Square Tensor Networks and Circuits Without Squaring Them

Authors: Lorenzo Loconte, Adrián Javaloy, Antonio Vergari

arXiv ID: 2512.17090 | Date: 2025-12-18

Abstract: Squared tensor networks (TNs) and their extension as computational graphs--squared circuits--have been used as expressive distribution estimators, yet supporting closed-form marginalization. However, the squaring operation introduces additional complexity when computing the partition function or marginalizing variables, which hinders their applicability in ML. To solve this issue, canonical forms of TNs are parameterized via unitary matrices to simplify the computation of marginals. However, these canonical forms do not apply to circuits, as they can represent factorizations that do not directly map to a known TN. Inspired by the ideas of orthogonality in canonical forms and determinism in circuits enabling tractable maximization, we show how to parameterize squared circuits to overcome their marginalization overhead. Our parameterizations unlock efficient marginalization even in factorizations different from TNs, but encoded as circuits, whose structure would otherwise make marginalization computationally hard. Finally, our experiments on distribution estimation show how our proposed conditions in squared circuits come with no expressiveness loss, while enabling more efficient learning.

Numerically exact open quantum system work statistics with process tensors

Authors: Mike Shubrook, Moritz Cygorek, Erik Gauger, Jake Iles-Smith, Ahsan Nazir

arXiv ID: 2512.16823 | Date: 2025-12-18

Abstract: Accurately quantifying the thermodynamic work costs of quantum operations is essential for the continued development and optimisation of emerging quantum technologies. This present a significant challenge in regimes of rapid control within complex, non-equilibrium environments - conditions under which many contemporary quantum devices operate and conventional approximations break down. Here, we introduce a process tensor framework that enables the computation of the full numerically exact quantum work statistics of driven open quantum systems. We demonstrate the utility of our approach by applying it to a Landauer erasure protocol operating beyond the weak-coupling, Markovian, and slow-driving limits. The resulting work probability distributions reveal distinct quantum signatures that are missed by low-order moments yet significantly impact the erasure fidelity of the protocol. Our framework delivers non-perturbative accuracy and detail in characterising energy-exchange fluctuations in driven open quantum systems, establishing a powerful and versatile tool for exploring thermodynamics and control in the operating regimes of both near-term and future quantum devices.

Topological magic response in quantum spin chains

Authors: Ritu Nehra, Poetri Sonya Tarabunga, Martina Frau, Mario Collura, Emanuele Tirrito, Marcello Dalmonte

arXiv ID: 2512.16673 | Date: 2025-12-18

Abstract: Topological matter provides natural platforms for robust, non-local information storage, central to quantum error correction. Yet, while the relation between entanglement and topology is well established, little is known about the role of nonstabilizerness (or magic), a pivotal concept in fault-tolerant quantum computation, in topological phases. We introduce the concept of topological magic response, the ability of a state to spread over stabilizer space when perturbed by finite-depth non-Clifford circuits. Unlike a topological invariant or order parameter, this response function probes how a phase reacts to non-Clifford perturbations, revealing the presence of non-local quantum correlations. In Ising-type spin chains, we show that symmetry-broken and paramagnetic phases lack such a response, whereas symmetry-protected topological (SPT) phases always display it. To capture this, we utilize a combination of stabilizer Rényi entropies that, in analogy with topological entanglement entropy, isolates non-locally stored information. Using exact analytic computations and matrix product states simulations based on an algorithmic technique we introduce, we show that SPT phases doped with TT gates support robust topological magic response, while trivial phases remain featureless.

Topological magic response in quantum spin chains

Authors: Ritu Nehra, Poetri Sonya Tarabunga, Martina Frau, Mario Collura, Emanuele Tirrito, Marcello Dalmonte

arXiv ID: 2512.16673 | Date: 2025-12-18

Abstract: Topological matter provides natural platforms for robust, non-local information storage, central to quantum error correction. Yet, while the relation between entanglement and topology is well established, little is known about the role of nonstabilizerness (or magic), a pivotal concept in fault-tolerant quantum computation, in topological phases. We introduce the concept of topological magic response, the ability of a state to spread over stabilizer space when perturbed by finite-depth non-Clifford circuits. Unlike a topological invariant or order parameter, this response function probes how a phase reacts to non-Clifford perturbations, revealing the presence of non-local quantum correlations. In Ising-type spin chains, we show that symmetry-broken and paramagnetic phases lack such a response, whereas symmetry-protected topological (SPT) phases always display it. To capture this, we utilize a combination of stabilizer Rényi entropies that, in analogy with topological entanglement entropy, isolates non-locally stored information. Using exact analytic computations and matrix product states simulations based on an algorithmic technique we introduce, we show that SPT phases doped with TT gates support robust topological magic response, while trivial phases remain featureless.

Tunable Topological Phases in an Organic One-Dimensional Mott Chain: Odd-Haldane (S = 1/2) and Haldane (S = 1)

Authors: Khalid N. Anindya, Hong Guo

arXiv ID: 2512.16173 | Date: 2025-12-18

Abstract: Establishing symmetry-protected topological (SPT) phases with interactions in chemically realistic systems remains an open challenge. We show that a single, synthetically plausible organic one-dimensional chain, tunable via chemical modification of its radical sites, hosts two such phases: an odd-Haldane phase of a dimerized S=12S=\tfrac{1}{2} Heisenberg chain and a Haldane phase of an S=1S=1 chain realized when Hund coupling locks two S=12S=\tfrac{1}{2} spins per monomer into S=1S=1. Density-functional theory places the active manifold deep in the Mott regime (U/t ⁣ ⁣126U/t\!\approx\!126), justifying a spin-only Heisenberg description; a compact (t,U) ⁣ ⁣J(t,U)\!\to\!J mapping then fixes exchange couplings. Exact diagonalization and DMRG reveal a consistent SPT fingerprint across both phases, including a quantized many-body Zak phase, even-degenerate entanglement spectrum, protected edge spins, and characteristic triplon/Haldane features in S+(q,ω)S^{+-}(q,ω). Our results identify a chemically programmable molecular platform for interacting SPT physics in one dimension and suggest concrete spectroscopic routes to organic Haldane spin chains for nanoscale quantum devices.

Tensor network approaches for plasma dynamics

Authors: Ryan J. J. Connor, Preetma Soin, Callum W. Duncan, Andrew J. Daley

arXiv ID: 2512.15924 | Date: 2025-12-17

Abstract: The dynamics of plasmas are governed by a set of non-linear differential equations which remain challenging to solve directly for large 2D and 3D problems. Here we investigate how tensor networks could be applied to plasmas described by the Vlasov-Maxwell system of equations and investigate parameter regimes which show promise for efficient simulations. We show for low-dimensional problems that the simplest form of tensor networks known as a Matrix Product State performs sufficiently well, however in regimes with a strong permanent magnetic field or high-dimensional problems one may need to consider alternative tensor network geometries. We conclude the study of the Vlasov-Maxwell system with the application of tensor networks to an industrially relevant test case and validate our results against state of the art plasma solvers based on Particle-In-Cell codes. We also extend the application of tensor networks to the alternative plasma description of Magnetohydrodynamics and outline how this can be encoded using Matrix Product States.

Anticoncentration and State Design of Doped Real Clifford Circuits and Tensor Networks

Authors: Beatrice Magni, Markus Heinrich, Lorenzo Leone, Xhek Turkeshi

arXiv ID: 2512.15880 | Date: 2025-12-17

Abstract: We investigate the statistical properties of orthogonal, or real, Clifford circuits doped with magic and imaginary resources. By developing the Weingarten calculus for the real Clifford group, we derive the exact overlap distribution of real stabilizer states, identifying a new universality class: the orthogonal Clifford Porter-Thomas distribution. We prove that local real architectures recover this global statistic in logarithmic depth. Furthermore, we uncover a sharp hierarchy in resource requirements: while retrieving Haar statistics necessitates a polylogarithmic amount of magic states, recovering the full unitary Clifford statistics requires only a single phase gate.

Tree Tensor Networks Methods for Efficient Calculation of Molecular Vibrational Spectra

Authors: Shuo Sun, Richard M. Milbradt, Stefan Knecht, Chandan Kumar, Christian B. Mendl

arXiv ID: 2512.15875 | Date: 2025-12-17

Abstract: We develop and employ general Tree Tensor Networks (TTNs) to compute the vibrational spectra for two model systems: a set of 64-dimensional coupled oscillators and acetonitrile. We explore various tree architectures, ranging from the simple linear structure of Matrix Product States (MPS), to trees where only the leaf nodes carry a physical leg -- as seen in the underlying ansatz of the Multilayer Multiconfiguration Time-Dependent Hartree (ML-MCTDH) method -- and further to more general trees in which all nodes are allowed to possess a physical leg. In addition, we implement Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) methods and Inverse Iteration methods as eigensolvers. By means of comprehensive benchmarking of runtime and accuracy, we demonstrate that sub-wavenumber accuracy in vibrational spectra is achievable with all TTN structures. MPS and three-legged tree tensor network states (T3NS) have similar runtimes, whereas leaf-only trees require significantly more time. All numerical simulations were performed using PyTreeNet, a Python package designed for flexible tensor network computations.

Solvable Quantum Circuits from Spacetime Lattices

Authors: Michael A. Rampp, Suhail A. Rather, Pieter W. Claeys

arXiv ID: 2512.15871 | Date: 2025-12-17

Abstract: In recent years dual-unitary circuits and their multi-unitary generalizations have emerged as exactly solvable yet chaotic models of quantum many-body dynamics. However, a systematic picture for the solvability of multi-unitary dynamics remains missing. We present a framework encompassing a large class of such non-integrable models with exactly solvable dynamics, which we term \emph{completely reducible} circuits. In these circuits, the entanglement membrane determining operator growth and entanglement dynamics can be characterized analytically. Completely reducible circuits extend the notion of space-time symmetry to more general lattice geometries, breaking dual-unitarity globally but not locally, and allow for a rich phenomenology going beyond dual-unitarity. As example, we introduce circuits that support four and five directions of information flow. We derive a general expression for the entanglement line tension in terms of the pattern of information flow in spacetime. The solvability is shown to be related to the absence of knots of this information flow, connecting entanglement dynamics to the Kauffman bracket as knot invariant. Building on these results, we propose that in general non-integrable dynamics the curvature of the entanglement line tension can be interpreted as a density of information transport. Our results provide a new and unified framework for exactly solvable models of many-body quantum chaos, encompassing and extending known constructions.

Large Isolated Stripes on Short 18-leg tt-JJ Cylinders

Authors: Tizian Blatz, Sebastian Paeckel, Ulrich Schollwöck, Fabian Grusdt, Annabelle Bohrdt

arXiv ID: 2512.15714 | Date: 2025-12-17

Abstract: Spin-charge stripes belong to the most prominent low-temperature orders besides superconductivity in high-temperature superconductors. This phase is particularly challenging to study numerically due to finite-size effects. By investigating the formation of long, isolated stripes, we offer a perspective complementary to typical finite-doping phase diagrams. We use the density-matrix renormalization group algorithm to extract the ground states of an 18-leg cylindrical strip geometry, making the diameter significantly wider than in previous works. This approach allows us to map out the range of possible stripe filling fractions on the electron versus hole-doped side. We find good agreement with established results, suggesting that the spread of filling fractions observed in the literature is governed by the physics of a single stripe. Taking a microscopic look at stripe formation, we reveal two separate regimes - a high-filling regime captured by a simplified squeezed-space model and a low-filling regime characterized by the structure of individual pairs of dopants. Thereby, we trace back the phenomenology of the striped phase to its microscopic constituents and highlight the different challenges for observing the two regimes in quantum simulation experiments.

Time integration of quantized tensor trains using the interpolative dynamical low-rank approximation

Authors: Erika Ye, Chao Yang

arXiv ID: 2512.15703 | Date: 2025-12-17

Abstract: Quantized tensor trains (QTTs) are a low-rank and multiscale framework that allows for efficient approximation and manipulation of multi-dimensional, high resolution data. One area of active research is their use in numerical simulation of hyperbolic systems such as the Navier-Stokes equations and the Vlasov equations. One popular time integration scheme is the dynamical low-rank approximation (DLRA), in which the time integration is constrained to a low-rank manifold. However, until recently, DLRA has typically used orthogonal projectors to project the original dynamical system into a reduced space, which is only well-suited for linear systems. DLRA has also mostly been investigated in the context of non-quantized tensor trains. This work investigates interpolative DLRA schemes in which the low-rank manifold is constructed from aptly chosen interpolation points and interpolating polynomials, in the context of QTTs. Through various examples, its performance is compared to its orthogonal counterpart. This work demonstrates how interpolative DLRA is suitable for nonlinear systems and time integrators requiring nonlinear element-wise operations, such as upwind time integration schemes.

Error mitigation for logical circuits using decoder confidence

Authors: Maria Dincă, Tim Chan, Simon C. Benjamin

arXiv ID: 2512.15689 | Date: 2025-12-17

Abstract: Fault-tolerant quantum computers use decoders to monitor for errors and find a plausible correction. A decoder may provide a decoder confidence score (DCS) to gauge its success. We adopt a swim distance DCS, computed from the shortest path between syndrome clusters. By contracting tensor networks, we compare its performance to the well-known complementary gap and find that both reliably estimate the logical error probability (LEP) in a decoding window. We explore ways to use this to mitigate the LEP in entire circuits. For shallow circuits, we just abort if any decoding window produces an exceptionally low DCS: for a distance-13 surface code, rejecting a mere 0.1% of possible DCS values improves the entire circuit's LEP by more than 5 orders of magnitude. For larger algorithms comprising up to trillions of windows, DCS-based rejection remains effective for enhancing observable estimation. Moreover, one can use DCS to assign each circuit's output a unique LEP, and use it as a basis for maximum likelihood inference. This can reduce the effects of noise by an order of magnitude at no quantum cost; methods can be combined for further improvements.

Space-Time Spectral Collocation Tensor-Network Approach for Maxwell's Equations

Authors: Dibyendu Adak, Rujeko Chinomona, Duc P. Truong, Oleg Korobkin, Kim Ø. Rasmussen, Boian S. Alexandrov

arXiv ID: 2512.15631 | Date: 2025-12-17

Abstract: In this work, we develop a space--time Chebyshev spectral collocation method for three-dimensional Maxwell's equations and combine it with tensor-network techniques in Tensor-Train (TT) format. Under constant material parameters, the Maxwell system is reduced to a vector wave equation for the electric field, which we discretize globally in space and time using a staggered spectral collocation scheme. The staggered polynomial spaces are designed so that the discrete curl and divergence operators preserve the divergence-free constraint on the magnetic field. The magnetic field is then recovered in a space--time post-processing step via a discrete version of Faraday's law. The global space--time formulation yields a large but highly structured linear system, which we approximate in low-rank TT-format directly from the operator and data, without assuming that the forcing is separable in space and time. We derive condition-number bounds for the resulting operator and prove spectral convergence estimates for both the electric and magnetic fields. Numerical experiments for three-dimensional electromagnetic test problems confirm the theoretical convergence rates and show that the TT-based solver maintains accuracy with approximately linear complexity in the number of grid points in space and time.

Fractional quantization by interaction of arbitrary strength in gapless flat bands with divergent quantum geometry

Authors: Wenqi Yang, Dawei Zhai, Wang Yao

arXiv ID: 2512.15041 | Date: 2025-12-17

Abstract: Fractional quantum anomalous Hall (FQAH) effect, a lattice analogue of fractional quantum Hall effect, offers a unique pathway toward fault-tolerant quantum computation and deep insights into the interplay of topology and strong correlations. The exploration has been successfully guided by the paradigm of ideal flat Chern bands, which mimic Landau levels in both band topology and local quantum geometry. Yet, given the near-infinite possibilities for Bloch bands in lattices, it remains a major open question whether FQAH states can emerge in scenarios fundamentally different from this paradigm. Here we turn to a class of gapless flat bands, featuring divergent quantum geometry at singular band touching, non-integer Berry flux threading the Brillouin zone (BZ), and ill-defined band topology. Our exact diagonalization and density matrix renormalization group calculations unambiguously demonstrate FQAH phase that is virtually independent of the interaction strength, persisting from the weak-interaction to the strong-interaction limit. We find the stability of the FQAH states does not uniquely correlate with the singularity strength or the BZ-averaged quantum geometric fluctuations. Instead, the many-body topological order can adapt to the singular and fluctuating quantum geometric landscape by spontaneously developing an inhomogeneous carrier distribution, while its quenching accompanies the drop in the occupation-weighted Berry flux. Our work reveals a profound interplay between quantum geometry and many-body correlation, and significantly expands the design space for exploring FQAH effect and flat-band correlation phenomena in general.

Dynamical Tensor Train Approximation for Kinetic Equations

Authors: Geshuo Wang, Jingwei Hu

arXiv ID: 2512.14950 | Date: 2025-12-16

Abstract: The numerical solution of kinetic equations is challenging due to the high dimensionality of the underlying phase space. In this paper, we develop a dynamical low-rank method based on the projector-splitting integrator in tensor-train (TT) format. The key idea is to discretize the three-dimensional velocity variable using tensor trains while treating the spatial variable as a parameter, thereby exploiting the low-rank structure of the distribution function in velocity space. In contrast to the standard step-and-truncate approach, this method updates the tensor cores through a sweeping procedure, allowing the use of relatively small TT-ranks and leading to substantial reductions in memory usage and computational cost. We demonstrate the effectiveness of the proposed approach on several representative kinetic equations.

A single-layer framework of variational tensor network states

Authors: Hongyu Chen, Yangfeng Fu, Weiqiang Yu, Rong Yu, Z. Y. Xie

arXiv ID: 2512.14414 | Date: 2025-12-16

Abstract: We propose a single-layer tensor network framework for the variational determination of ground states in two-dimensional quantum lattice models. By combining the nested tensor network method [Phys. Rev. B 96, 045128 (2017)] with the automatic differentiation technique, our approach can reduce the computational cost by three orders of magnitude in bond dimension, and therefore enables highly efficient variational ground-state calculations. We demonstrate the capability of this framework through two quantum spin models: the antiferromagnetic Heisenberg model on a square lattice and the frustrated Shastry-Sutherland model. Even without GPU acceleration or symmetry implimention, we have achieved the bond dimension of 9 and obtained accurate ground-state energy and consistent order parameters compared to prior studies. In particular, we confirm the existence of an intermediate empty-plaquette valence bond solid ground state in the Shastry-Sutherland model. We have further discussed the convergence of the algorithm and its potential improvements. Our work provides a promising route for large-scale tensor network calculations of two-dimensional quantum systems.

Simplex Crystal Ground State and Magnetization Plateaus in the Spin-1/21/2 Heisenberg Model on the Ruby Lattice

Authors: Pratyay Ghosh, Frédéric Mila

arXiv ID: 2512.14173 | Date: 2025-12-16

Abstract: We investigate the spin-1/21/2 Heisenberg antiferromagnet on the ruby lattice with uniform first- and second-neighbor interactions, which forms a two-dimensional network of corner-sharing tetrahedra. Using infinite projected entangled pair states (iPEPS), we study the ground state of the system to find that it assumes a gapped threefold-degenerate simplex crystal ground state, with strong singlets formed on pairs of neighboring triangles. We argue that the formation of the simplex singlet ground state at the isotropic point relates to the weak inter-triangle coupling limit where an effective spin-chirality Hamiltonian on the honeycomb lattice exhibits an extensively degenerate ground state manifold of singlet coverings at the mean-field level. Under an applied Zeeman field, the iPEPS simulations uncover magnetization plateaus at m/ms=0,1/3,1/2,m/m_s = 0, 1/3, 1/2, and 2/32/3, separated by intermediate supersolid phases, all breaking the sixfold rotational symmetry of the lattice. Unlike the checkerboard lattice, these plateaus cannot be described by strongly localized magnons.

A sine-square deformation approach to quantum critical points in one-dimensional systems

Authors: Yuki Miyazaki, Shiori Tanigawa, Giacomo Marmorini, Nobuo Furukawa, Daisuke Yamamoto

arXiv ID: 2512.14149 | Date: 2025-12-16

Abstract: We propose a method to determine the quantum phase boundaries of one-dimensional systems using sine-square deformation (SSD). Based on the proposition, supported by several exactly solved cases though not proven in full generality, that "if a one-dimensional system is gapless, then the expectation value of any local observable in the ground state of the Hamiltonian with SSD exhibits translational symmetry in the thermodynamic limit," we determine the quantum critical point as the location where a local observable becomes site-independent, identified through finite-size scaling analysis. As case studies, we consider two models: the antiferromagnetic Ising chain in mixed transverse and longitudinal magnetic fields with nearest-neighbor and long-range interactions. We calculate the ground state of these Hamiltonians with SSD using the density-matrix renormalization-group algorithm and evaluate the local transverse magnetization. For the nearest-neighbor model, we show that the quantum critical point can be accurately estimated by our procedure with systems of up to 84 sites, or even smaller, in good agreement with results from the literature. For the long-range model, we find that the phase boundary between the antiferromagnetic and paramagnetic phases is slightly shifted relative to the nearest-neighbor case, leading to a reduced region of antiferromagnetic order. Moreover, we propose an experimental procedure to implement the antiferromagnetic J1J_1-J2J_2 Ising couplings with SSD using Rydberg atom arrays in optical tweezers, which can be achieved within a very good approximation. Because multiple independent scaling conditions naturally emerge, our approach enables precise determination of quantum critical points and possibly even the extraction of additional critical phenomena, such as critical exponents, from relatively small system sizes.

Correlation functions at the topological quantum phase transition in the S=1 XXZ chain with single-ion anisotropy

Authors: Toshiya Hikihara, Akira Furusaki

arXiv ID: 2512.14075 | Date: 2025-12-16

Abstract: We study the one-dimensional S=1 XXZ spin model with single-ion anisotropy. It is known that at the transition points between the Haldane and large-D phases, the model exhibits a quantum criticality described by the Gaussian theory, i.e., a conformal field theory with the central charge c=1. Using the bosonization approach, we investigate various correlation functions at the phase transition and derive their asymptotic forms. This allows us to clarify their peculiar behavior: the longitudinal (transverse) two-point spin correlation function has components that decay algebraically only in the uniform (staggered) sector. These theoretical predictions are verified by the numerical calculations using the density-matrix renormalization group method. The effect of weak bond alternation on the critical ground state at the phase transition is also discussed. It is shown that the bond alternation induces the missing power-law components in the correlation functions.

Algorithmic aspects of gauged Gaussian fermionic projected entangled pair states

Authors: Itay Gomelski, Jonathan Elyovich, Ariel Kelman, Erez Zohar, Patrick Emonts

arXiv ID: 2512.13812 | Date: 2025-12-15

Abstract: Lattice gauge theories (LGTs) provide a powerful framework for studying non-perturbative phenomena in gauge theories. However, conventional approaches such as Monte Carlo (MC) simulations in imaginary time are limited, as they do not allow real time evolution and suffer from a sign problem in many important cases. Using Gauged Gaussian fermionic projected entangled pair states (GGFPEPS) as a variational ground state ansatz offers an alternative for studying LGTs through a sign-problem-free variational MC. As this method is extended to larger and more complex systems, understanding its numerical behavior becomes essential. While conventional action based MC has been extensively studied, the performance and characteristics of non-action-based MC within the GGFPEPS framework are far less explored. In this work, we investigate these algorithmic aspects, identifying an optimal update size for GGFPEPS-based MC simulations for Z2\mathbb{Z}_2 in 2+12+1 dimensions. We show that gauge fixing generally slows convergence, and demonstrate that not exploiting the translation-invariance can, in some cases, improve the computational time scaling of error convergence. We expect that these improvements will allow advancing the simulation to larger and more complex systems.

Non-hermitian Density Matrices from Time-like Entanglement and Wormholes

Authors: Jonathan Harper, Taishi Kawamoto, Ryota Maeda, Nanami Nakamura, Tadashi Takayanagi

arXiv ID: 2512.13800 | Date: 2025-12-15

Abstract: We extensively explore the connections between time-like entanglement and non-hermitian density matrices in quantum many-body systems. We classify setups where we encounter non-hermitian density matrices into two types: one is due to causal influences under unitary evolutions, and the other is due to non-unitary evolutions in non-hermitian systems. We provide various examples of these setups including interacting harmonic oscillators, two dimensional conformal field theories and holographic dualities. In them, we compute the time-like entanglement entropy and imagitivity, which measures how much density matrices are non-hermitian. In both two classes, typical holographic examples are given by traversable AdS wormholes. We explain how causal influences in a wormhole dual to a pair of non-hermitian quantum systems is possible even without interactions between them. We argue that to realize a traversable wormhole we need not only ordinary quantum entanglement but also time-like entanglement.

Magnetism and superconductivity in bilayer nickelate

Authors: Hui Yang, Ya-Hui Zhang

arXiv ID: 2512.13793 | Date: 2025-12-15

Abstract: The discovery of high-temperature superconductivity in bilayer nickelate La3_{3}Ni2_{2}O7_{7} necessitates a minimal theoretical model that unifies the superconducting phase with the spin-density-wave (SDW) phase without external pressure or strain. We propose a model where half-filled dz2d_{z^{2}} local moments interact with itinerant dx2y2d_{x^{2}-y^{2}} electrons via strong Hund's coupling JHJ_H, which reduces to a bilayer type-II t-J model in the large JHJ_H limit. Using iDMRG calculations on an Ly=4,Lz=2L_y=4, L_z=2 cylinder, we demonstrate that the competition between double-exchange ferromagnetism and in-plane superexchange generates period-4 stripe-like SDW order-a feature absent in one-orbital t-J model with only dx2y2d_{x^2-y^2} orbital. Furthermore, increasing the interlayer exchange coupling suppresses magnetic order and stabilizes interlayer s-wave superconductivity. These results identify the type-II t-J model as a minimal framework for capturing the interplay of magnetism and superconductivity in bilayer nickelates.

Matrix Product State Simulation of Reacting Shear Flows

Authors: Robert Pinkston, Nikita Gourianov, Hirad Alipanah, Peyman Givi, Dieter Jaksch, Juan Jose Mendoza-Arenas

arXiv ID: 2512.13661 | Date: 2025-12-15

Abstract: Direct numerical simulation (DNS) of turbulent reactive flows has been the subject of significant research interest for several decades. Accurate prediction of the effects of turbulence on the rate of reactant conversion, and the subsequent influence of chemistry on hydrodynamics remain a challenge in combustion modeling. The key issue in DNS is to account for the wide range of temporal and spatial physical scales that are caused by complex interactions of turbulence and chemistry. In this work, a new computational methodology is developed that is shown to provide a viable alternative to DNS. The framework is the matrix product state (MPS), a form of tensor network (TN) as used in computational many body physics. The MPS is a well-established ansatz for efficiently representing many types of quantum states in condensed matter systems, allowing for an exponential compression of the required memory compared to exact diagonalization methods. Due to the success of MPS in quantum physics, the ansatz has been adapted to problems outside its historical domain, notably computational fluid dynamics. Here, the MPS is used for computational simulation of a shear flow under non-reacting and nonpremixed chemically reacting conditions. Reductions of 30% in memory are demonstrated for all transport variables, accompanied by excellent agreements with DNS. The anastaz accurately captures all pertinent flow physics such as reduced mixing due to exothermicity & compressibility, and the formation of eddy shocklets at high Mach numbers. A priori analysis of DNS data at higher Reynolds numbers shows compressions as large as 99.99% for some of the transport variables. This level of compression is encouraging and promotes the use of MPS for simulations of complex turbulent combustion systems.

A homogeneous geometry of low-rank tensors

Authors: Simon Jacobsson

arXiv ID: 2512.13594 | Date: 2025-12-15

Abstract: We consider sets of fixed CP, multilinear, and TT rank tensors, and derive conditions for when (the smooth parts of) these sets are smooth homogeneous manifolds. For CP and TT ranks, the conditions are essentially that the rank is sufficiently low. These homogeneous structures are then used to derive Riemannian metrics whose geodesics are both complete and efficient to compute.

Tensor Network Formulation of Dequantized Algorithms for Ground State Energy Estimation

Authors: Hidetaka Manabe, Takanori Sugimoto, Keisuke Fujii

arXiv ID: 2512.13548 | Date: 2025-12-15

Abstract: Verifying quantum advantage for practical problems, particularly the ground state energy estimation (GSEE) problem, is one of the central challenges in quantum computing theory. For that purpose, dequantization algorithms play a central role in providing a clear theoretical framework to separate the complexity of quantum and classical algorithms. However, existing dequantized algorithms typically rely on sampling procedures, leading to prohibitively large computational overheads and hindering their practical implementation on classical computers. In this work, we propose a tensor network-based dequantization framework for GSEE that eliminates the sampling process while preserving the asymptotic complexity of prior dequantized algorithms. In our formulation, the overhead arising from sampling is replaced by the growth of the bond dimension required to represent Chebyshev vectors as tensor network states. Consequently, physical structure, such as entanglement and locality, is naturally reflected in the computational cost. By combining this approach with tensor network approximations, such as Matrix Product States (MPS), we construct a practical dequantization algorithm that is executable within realistic computational resources. Numerical simulations demonstrate that our method can efficiently construct high-degree polynomials up to d=104d=10^4 for Hamiltonians with up to 100100 qubits, explicitly revealing the crossover between classically tractable and quantum advantaged regimes. These results indicate that tensor network-based dequantization provides a crucial tool toward the rigorous, quantitative verification of quantum advantage in realistic many-body systems.

A Joint Quantum Computing, Neural Network and Embedding Theory Approach for the Derivation of the Universal Functional

Authors: Martin J. Uttendorfer, Daniel Barragan-Yani, Matthias Sperl, Marc Landmann

arXiv ID: 2512.13138 | Date: 2025-12-15

Abstract: We introduce a novel approach that exploits the intersection of quantum computing, machine learning and reduced density matrix functional theory to leverage the potential of quantum computing to improve simulations of interacting quantum particles. Our method focuses on obtaining the universal functional using a deep neural network trained with quantum algorithms. We also use fragment-bath systems defined by density matrix embedding theory to strengthen our approach by substantially expanding the space of Hamiltonians for which the obtained functional can be applied without the need for additional quantum resources. Given the fact that once obtained, the same universal functional can be reused for any system where the interactions within the embedded fragment are identical, our work demonstrates a way to potentially achieve a cumulative quantum advantage within quantum computing applications for quantum chemistry and condensed matter physics.

Autoregressive Neural Network Extrapolation of Quantum Spin Dynamics Across Time and Space

Authors: Hubert Pugzlys, Shreyas Varude, Sam Dillon, Huy Tran, Ta Tang, Zhe Jiang, Xuzhe Ying, Chunjing Jia

arXiv ID: 2512.13103 | Date: 2025-12-15

Abstract: Understanding the dynamical response of quantum materials is central to revealing their microscopic properties, yet access to long-time and large-scale dynamics remains severely limited by rapidly growing computational costs and entanglement, particularly in gapless systems. Here we introduce an autoregressive machine-learning framework that enables the extrapolation of dynamical spin correlations in both time and space beyond the reach of conventional numerical methods. Trained on time-dependent density matrix renormalization group simulations of the gapless XXZ model, our approach is benchmarked against exact solutions available for this analytically solvable system. Combined with physics-informed spatial extension, multi-layer perceptron model using ReLU activation functions has been shown to be superior than convolutional neural networks and linear regressions for longer time extrapolation. Perturbation study of error accumulation further demonstrates that our autoregressive neural network extrapolations are highly robust to perturbations, suggesting stable and reliable predictions. This work establishes a new paradigm for studying the dynamics of gapless quantum many-body systems, in which machine learning extends and complements the capabilities of state-of-the-art numerical approaches.

Holographic Codes from Enriched Link Entanglement in Spin Networks

Authors: Mai Qi, Eugenia Colafranceschi

arXiv ID: 2512.12927 | Date: 2025-12-15

Abstract: We introduce an enriched entanglement structure for spin networks, inspired by tensor-network constructions, in which internal links can carry a controlled and discrete amount of entanglement. In the spin-network picture, vertices are dual to simplices and links are dual to their faces. Standard spin-network gluing corresponds to fully identifying two simplices along a face, implemented by a maximally entangled, gauge-invariant singlet state on the corresponding link, while unglued faces correspond to links carrying no entanglement. Working on a complete graph, we promote this binary choice to a controlled and tunable structure by allowing each link to carry a variable amount of entanglement, interpolating between product states and the fully entangled singlet. The additional link variables therefore control not only the amount of entanglement but also the extent to which gauge invariance at internal links is preserved or broken, admitting an interpretation in terms of emergent edge-mode-like degrees of freedom. Within this framework, spin-network contraction defines a bulk-to-boundary map from link-entanglement data to boundary states. Adapting techniques developed in random tensor networks, we show that in a suitable large-spin regime the map is a co-isometry in expectation value. Restricting to a code subspace defined by configurations in which links are either effectively glued or open, with small fluctuations around this pattern, the map becomes an exact isometry. This yields a discrete and geometrically meaningful realization of holographic and error-correcting features within the spin-network Hilbert space.

Uniform matrix product states with a boundary

Authors: Marta Florido-Llinàs, Álvaro M. Alhambra, David Pérez-García, J. Ignacio Cirac

arXiv ID: 2512.11968 | Date: 2025-12-12

Abstract: Canonical forms are central to the analytical understanding of tensor network states, underpinning key results such as the complete classification of one-dimensional symmetry-protected topological phases within the matrix product state (MPS) framework. Yet, the established theory applies only to uniform MPS with periodic boundary conditions, leaving many physically relevant states beyond its reach. Here we introduce a generalized canonical form for uniform MPS with a boundary matrix, thus extending the analytical MPS framework to a more general setting of wider physical significance. This canonical form reveals that any such MPS can be represented as a block-invertible matrix product operator acting on a structured class of algebraic regular language states that capture its essential long-range and scale-invariant features. Our construction builds on new algebraic results of independent interest that characterize the span and algebra generated by non-semisimple sets of matrices, including a generalized quantum Wielandt's inequality that gives an explicit upper bound on the blocking length at which the fixed-length span stabilizes to an algebra. Together, these results establish a unified theoretical foundation for uniform MPS with boundaries, bridging the gap between periodic and arbitrary-boundary settings, and providing the basis for extending key analytical and classification results of matrix product states to a much broader class of states and operators.

Holographic Representation of One-Dimensional Many-Body Quantum States via Isometric Tensor Networks

Authors: Kaito Kobayashi, Benjamin Sappler, Frank Pollmann

arXiv ID: 2512.11967 | Date: 2025-12-12

Abstract: Isometric tensor network states (isoTNS) allow for efficient and accurate simulations of higher-dimensional quantum systems by enforcing an isometric structure. We bring this idea back to one dimension by introducing a holographic isoTNS ansatz: a (1+1)-dimensional lattice of isometric tensors where the horizontal axis encodes physical space and an auxiliary "holographic" axis boosts expressivity. Despite the enlarged geometry, contractions and local updates remain computationally efficient due to isometric constraints. We investigate this ansatz and benchmark it in comparison to matrix product states (MPS). First, we show that randomly initialized holographic isoTNS typically display volume-law entanglement even at modest bond dimension, surpassing the representational limits of MPS and related ansätze. Second, through analytic constructions and variational optimization, we demonstrate that holographic isoTNS can faithfully represent arbitrary fermionic Gaussian states, Clifford states, and certain short-time-evolved states under local evolution -- a family of states that is highly entangled but low in complexity. Third, to exploit this expressivity in broad situations, we implement a time-evolving block decimation (TEBD) algorithm on holographic isoTNS. While the method remains efficient and scalable, error accumulation over TEBD sweeps suppresses entanglement and leads to rapid deviations from exact dynamics. Overall, holographic isoTNS broaden the reach of tensor-network methods, opening new avenues to study physics in the volume-law regime.

Spatiotemporal scales of dynamical quantum phase transitions in the Bose-Hubbard model

Authors: Jia Li, Yajiang Hao

arXiv ID: 2512.11314 | Date: 2025-12-12

Abstract: We investigate the spatial and temporal scales of dynamical quantum phase transitions in the one-dimensional Bose-Hubbard model in the strong interaction limit. Using Jordan-Wigner transformation, we obtain the time-dependent wavefunction and therefore the subsystem Loschmidt echo, and systematically investigate how its properties vary with subsystem size. It is found that when the subsystem is sufficiently large, it exhibits logarithmic divergence identical to that of the full system Loschmidt echo, yielding a critical exponent of zero. We also obtain the required subsystem size and temporal resolution for detecting dynamical quantum phase transitions using the subsystem Loschmidt echo. It is expected that the present results provide a reliable foundation for further experimental investigations.

Symmetry-protected topological scar subspaces

Authors: Chihiro Matsui, Thomas Quella, Naoto Tsuji

arXiv ID: 2512.11216 | Date: 2025-12-12

Abstract: We propose a framework that extends the notion of symmetry-protected topological properties beyond the ground-state paradigm to dynamically isolated subspaces formed by exceptional non-thermal energy eigenstates of non-integrable systems, known as quantum many-body scars (QMBS). We introduce the concept of a symmetry-protected topological (SPT) scar subspace -- a Hilbert subspace stabilized by a restricted spectrum-generating algebra (rSGA) while being protected by on-site, inversion, and time-reversal symmetries. QMBS often admit a non-interacting quasiparticle description, which enables matrix-product representations with small bond dimension. Although individual QMBS do not necessarily retain the protecting symmetries of the Hamiltonian, we show that the subspace formed by the symmetry-connected QMBS does retain them, giving rise to consistently emerging topological properties across the entire scar subspace. Using the spin-11 Affleck--Kennedy--Lieb--Tasaki (AKLT) model, we demonstrate that its bimagnon scar subspace reflects the topological properties of the SPT ground state, as evidenced by the appropriate bond-space symmetry representations, the expected topological response, and the numerically verified long-range string order. Our findings indicate that scar subspaces can inherit -- and in inhomogeneous cases systematically modify -- the topological character of the SPT ground state, offering a new and experimentally accessible platform for probing symmetry-protected topology beyond the ground-state regime.

Partitioned Expansions for Approximate Tensor Network Contractions

Authors: Glen Evenbly, Johnnie Gray, Garnet Kin-Lic Chan

arXiv ID: 2512.10910 | Date: 2025-12-11

Abstract: We propose a method for approximating the contraction of a tensor network by partitioning the network into a sum of computationally cheaper networks. This method, which we call a partitioned network expansion (PNE), builds upon recent work that systematically improves belief propagation (BP) approximations using loop corrections. However, in contrast to previous approaches, our expansion does not require a known BP fixed point to be implemented and can still yield accurate results even in cases where BP fails entirely. The flexibility of our approach is demonstrated through applications to a variety of example networks, including finite 2D and 3D networks, infinite networks, networks with open indices, and networks with degenerate BP fixed points. Benchmark numerical results for networks composed of Ising, AKLT, and random tensors typically show an improvement in accuracy over BP by several orders of magnitude (when BP solutions are obtainable) and also demonstrate improved performance over traditional network approximations based on singular value decomposition (SVD) for certain tasks.

Hybrid quantum-classical matrix-product state and Lanczos methods for electron-phonon systems with strong electronic correlations: Application to disordered systems coupled to Einstein phonons

Authors: Heiko Georg Menzler, Suman Mondal, Fabian Heidrich-Meisner

arXiv ID: 2512.10899 | Date: 2025-12-11

Abstract: We present two quantum-classical hybrid methods for simulating the time-dependence of electron-phonon systems that treat electronic correlations numerically exactly and optical-phonon degrees of freedom classically. These are a time-dependent Lanczos and a matrix-product state method, each combined with the multi-trajectory Ehrenfest approach. Due to the approximations, reliable results are expected for the adiabatic regime of small phonon frequencies. We discuss the convergence properties of both methods for a system of interacting spinless fermions in one dimension and provide a benchmark for the Holstein chain. As a first application, we study the decay of charge density wave order in a system of interacting spinless fermions coupled to Einstein oscillators and in the presence of quenched disorder. We investigate the dependence of the relaxation dynamics on the electron-phonon coupling strength and provide numerical evidence that the coupling of strongly disordered systems to classical oscillators leads to delocalization, thus destabilizing the (finite-size) many-body localization in this system.

Phase structure of the one-dimensional Z2\mathbb{Z}_2 lattice gauge theory with second nearest-neighbor interactions

Authors: Yeimer Zambrano, Aleksey Alekseev, Konrad J. Kapcia, Krzysztof Cichy, Agnieszka Cichy

arXiv ID: 2512.10755 | Date: 2025-12-11

Abstract: We investigate the ground-state phase diagram of a one-dimensional Z2\mathbb{Z}_2 lattice gauge theory (LGT) model with hard-core bosons at half-filling, extending previous studies by including second nearest-neighbor (2NN) interactions. Using matrix product state techniques within the density matrix renormalization group, we compute charge gap, static structure factor, and pair-pair correlation functions for various interaction strengths and field parameters. We analyze two representative neatest-neighbor interaction strengths (V1V_1) that correspond to the Luttinger liquid (LL) and Mott insulator (MI) phases in the absence of the 2NN interactions. We introduce the 2NN coupling V2V_2 and investigate its impact on the system. Our results reveal very rich behavior. As the 2NN repulsion increases, in the case of small V1V_1, we observe a direct transition from the LL phase to a charge-ordered insulator (COI) phase, whereas for large V1V_1, we observe a transition from the MI phase (previously found with only V1V_1 included), going through an intermediate LL region, and finally reaching the COI regime. Additionally, the inclusion of 2NN interactions enhances charge order and suppresses pair coherence, evidenced by sharp peaks in the structure factor and rapid decay in pair-pair correlators. Our work extends the well-studied phase structure of 1D Z2\mathbb{Z}_2 LGT models and demonstrates the interplay between gauge fields, confinement, and extended interactions.

Efficient simulation of low-entanglement bosonic Gaussian states in polynomial time

Authors: Tong Liu, Hui-Ke Jin, Tao Xiang, Hong-Hao Tu

arXiv ID: 2512.10643 | Date: 2025-12-11

Abstract: Bosonic Gaussian states appear ubiquitously in quantum optics and condensed matter physics but remain difficult to simulate classically due to the hafnian bottleneck. We present an efficient algorithm that converts pure bosonic Gaussian states into matrix product states (MPSs), with a computational cost governed solely by the entanglement and not by the number of bosonic modes. Our method combines a Gaussian singular value decomposition with a projected-creation-operator mapping that constructs local MPS tensors without computing hafnians. Benchmarking on covariance matrices from the Jiuzhang 2.0 and Jiuzhang 4.0 Gaussian boson sampling experiments demonstrates substantial speedups over previous tensor-network approaches in the low-entanglement regime relevant to lossy devices. The method provides a scalable classical simulation framework for bosonic Gaussian states with limited entanglement and extends the applicability of MPS-based methods to a broad range of bosonic systems.

Stability of the symmetry-protected topological phase and Ising transitions in a disordered U(1) quantum link model on a ladder

Authors: Mykhailo V. Rakov, Luca Tagliacozzo, Maciej Lewenstein, Jakub Zakrzewski, Titas Chanda

arXiv ID: 2512.10642 | Date: 2025-12-11

Abstract: We revisit the U(1) quantum link model in a ladder geometry, finding, by finite-size scaling, that the critical exponent ν=1ν=1 and the central charge c=1/2c=1/2 are consistent with the Ising universality class for all phase transitions observed. A blind application of the Harris criterion would suggest that this criticality is lost in the presence of the disorder. It turns out not to be the case. For the disorder affecting ladder's rung hoppings only, we have found that the transitions survive disappearing only for quite strong disorder. The disorder in the ladder's legs destroys the nonzero mass phase criticality, while the symmetry-protected topological phase for zero mass survives a small disorder. The observed robustness against disorder is explained qualitatively using field-theoretic arguments.

Tracking large chemical reaction networks and rare events by neural networks

Authors: Jiayu Weng, Xinyi Zhu, Jing Liu, Linyuan Lü, Pan Zhang, Ying Tang

arXiv ID: 2512.10309 | Date: 2025-12-11

Abstract: Chemical reaction networks are widely used to model stochastic dynamics in chemical kinetics, systems biology and epidemiology. Solving the chemical master equation that governs these systems poses a significant challenge due to the large state space exponentially growing with system sizes. The development of autoregressive neural networks offers a flexible framework for this problem; however, its efficiency is limited especially for high-dimensional systems and in scenarios with rare events. Here, we push the frontier of neural-network approach by exploiting faster optimizations such as natural gradient descent and time-dependent variational principle, achieving a 5- to 22-fold speedup, and by leveraging enhanced-sampling strategies to capture rare events. We demonstrate reduced computational cost and higher accuracy over the previous neural-network method in challenging reaction networks, including the mitogen-activated protein kinase (MAPK) cascade network, the hitherto largest biological network handled by the previous approaches of solving the chemical master equation. We further apply the approach to spatially extended reaction-diffusion systems, the Schlögl model with rare events, on two-dimensional lattices, beyond the recent tensor-network approach that handles one-dimensional lattices. The present approach thus enables efficient modeling of chemical reaction networks in general.

Error Mitigation of Fault-Tolerant Quantum Circuits with Soft Information

Authors: Zeyuan Zhou, Shaun Pexton, Aleksander Kubica, Yongshan Ding

arXiv ID: 2512.09863 | Date: 2025-12-10

Abstract: Quantum error mitigation (QEM) is typically viewed as a suite of practical techniques for today's noisy intermediate-scale quantum devices, with limited relevance once fault-tolerant quantum computers become available. In this work, we challenge this conventional wisdom by showing that QEM can continue to provide substantial benefits in the era of quantum error correction (QEC), and in an even more efficient manner than it does on current devices. We introduce a framework for logical-level QEM that leverages soft information naturally produced by QEC decoders, requiring no additional data, hardware modifications, or runtime overhead beyond what QEC protocols already provide. Within this framework, we develop and analyze three logical-level QEM techniques: post-selection and runtime abort policies, probabilistic error cancellation, and zero-noise extrapolation. Our techniques reduce logical error rates by more than 100x while discarding fewer than 0.1% of shots; they also provide in situ characterization of logical channels for QEM protocols. As a proof of principle, we benchmark our approach using a surface-code architecture and two state-of-the-art decoders based on tensor-network contraction and minimum-weight perfect matching. We evaluate logical-level QEM on random Clifford circuits and molecular simulation algorithms and find that, compared to previous approaches relying on QEC only or QEC combined with QEM, we can achieve up to 87.4% spacetime overhead savings. Our results demonstrate that logical-level QEM with QEC decoder soft information can reliably improve logical performance, underscoring the efficiency and usefulness of QEM techniques for fault-tolerant quantum computers.

Optyx: A ZX-based Python library for networked quantum architectures

Authors: Mateusz Kupper, Richie Yeung, Boldizsár Poór, Alexis Toumi, William Cashman, Giovanni de Felice

arXiv ID: 2512.09648 | Date: 2025-12-10

Abstract: Distributed, large-scale quantum computing will need architectures that combine matter-based qubits with photonic links, but today's software stacks target either gate-based chips or linear-optical devices in isolation. We introduce Optyx, an open-source Python framework offering a unified language to program, simulate, and prototype hybrid, networked systems: users create experiments that mix qubit registers, discrete-variable photonic modes, lossy channels, heralded measurements, and real-time feedback; Optyx compiles them via ZX/ZW calculus into optimised tensor-network forms, and executes with state-of-the-art contraction schedulers based on Quimb and Cotengra. Benchmarking on exact multi-photon circuit simulations shows that, versus permanent-based methods, tensor network contraction can deliver speedups of orders of magnitude for low-depth circuits and entangled photon sources, and natively supports loss and distinguishability -- establishing it as both a high-performance simulator and a rapid-prototyping environment for next-generation photonic-network experiments.

Tensor-Compressed and Fully-Quantized Training of Neural PDE Solvers

Authors: Jinming Lu, Jiayi Tian, Yequan Zhao, Hai Li, Zheng Zhang

arXiv ID: 2512.09202 | Date: 2025-12-10

Abstract: Physics-Informed Neural Networks (PINNs) have emerged as a promising paradigm for solving partial differential equations (PDEs) by embedding physical laws into neural network training objectives. However, their deployment on resource-constrained platforms is hindered by substantial computational and memory overhead, primarily stemming from higher-order automatic differentiation, intensive tensor operations, and reliance on full-precision arithmetic. To address these challenges, we present a framework that enables scalable and energy-efficient PINN training on edge devices. This framework integrates fully quantized training, Stein's estimator (SE)-based residual loss computation, and tensor-train (TT) decomposition for weight compression. It contributes three key innovations: (1) a mixed-precision training method that use a square-block MX (SMX) format to eliminate data duplication during backpropagation; (2) a difference-based quantization scheme for the Stein's estimator that mitigates underflow; and (3) a partial-reconstruction scheme (PRS) for TT-Layers that reduces quantization-error accumulation. We further design PINTA, a precision-scalable hardware accelerator, to fully exploit the performance of the framework. Experiments on the 2-D Poisson, 20-D Hamilton-Jacobi-Bellman (HJB), and 100-D Heat equations demonstrate that the proposed framework achieves accuracy comparable to or better than full-precision, uncompressed baselines while delivering 5.5x to 83.5x speedups and 159.6x to 2324.1x energy savings. This work enables real-time PDE solving on edge devices and paves the way for energy-efficient scientific computing at scale.

Optimizing the dynamical preparation of quantum spin lakes on the ruby lattice

Authors: DinhDuy Vu, Dominik S. Kufel, Jack Kemp, Lode Pollet, Chris R. Laumann, Norman Y. Yao

arXiv ID: 2512.09040 | Date: 2025-12-09

Abstract: Quantum spin liquids are elusive long-range entangled states. Motivated by experiments in Rydberg quantum simulators, recent excitement has centered on the possibility of dynamically preparing a state with quantum spin liquid correlation even when the ground state phase diagram does not exhibit such a topological phase. Understanding the microscopic nature of such quantum spin "lake" states and their relationship to equilibrium spin liquid order remains an essential question. Here, we extend the use of approximately symmetric neural quantum states for real-time evolution and directly simulate the dynamical preparation in systems of up to N=384N=384 atoms. We analyze a variety of spin liquid diagnostics as a function of the preparation protocol and optimize the extent of the quantum spin lake thus obtained. In the optimal case, the prepared state shows spin-liquid properties extending over half the system size, with a topological entanglement entropy plateauing close to γ=ln2γ= \ln 2. We extract two physical length scales λλ and ξξ which constrain the extent of the quantum spin lake \ell from above and below.

Microscopic Theory Revealing Dual Field-Induced Transitions in Spin-1/2 Screw-Chain Magnets

Authors: Mandev Bhullar, Philip Richard, Hae-Young Kee

arXiv ID: 2512.09039 | Date: 2025-12-09

Abstract: We develop a microscopic theory for pseudospin-12\frac{1}{2} screw-chain compounds with spin-orbit coupling that goes beyond the phenomenological site-dependent gg-tensor description traditionally used for XXZ-like BaCo2_2V2_2O8_8 and related materials. Starting from the symmetry-allowed JKΓJKΓ Hamiltonian with Heisenberg JJ, Kitaev KK, and off-diagonal ΓΓ interactions, we show that the ΓΓ interaction naturally generates the four-sublattice pattern associated with the crystal's screw symmetry. Using the density matrix renormalization group, we identify two distinct field-induced transitions. The first is a continuous transition into an intermediate phase, where the symmetry responsible for the two-fold ground-state degeneracy is broken. The second is a first-order transition into the high-field phase, characterized by a discontinuous jump in the spin-spin correlator. Entanglement-entropy scaling confirms that the first transition belongs to the Ising critical point with the central charge 1/21/2. These results establish a microscopic framework for pseudospin-12\frac{1}{2} screw-chain systems such as Co2+^{2+} materials, uncover an intermediate phase whose width increases with ΓΓ, and provide guidance for systematic exploration of additional field orientations and structural distortions.

Extreme statistics as a probe of the superfluid to Bose-glass Berezinskii-Kosterlitz-Thouless transition

Authors: Jeanne Colbois, Natalia Chepiga, Shaffique Adam, Gabriel Lemarié, Nicolas Laflorencie

arXiv ID: 2512.09029 | Date: 2025-12-09

Abstract: Recent studies of delocalization-localization transitions in disordered quantum chains have highlighted the role of rare, chain-breaking events that favor localization, in particular for high-energy eigenstates related to many-body localization. In this context, we revisit the random-field XXZ spin-1/2 chain at zero temperature with ferromagnetic interactions, equivalent to interacting fermions or hard-core bosons in a random potential with attractive interactions. We argue that localization in this model can be characterized by chain-breaking events, which are probed by the extreme values of simple local observables, such as the on-site density or the local magnetization, that are readily accessible in both experiments and numerical simulations. Adopting a bosonic language, we study the disorder-induced Berezinskii-Kosterlitz-Thouless (BKT) quantum phase transition from superfluid (SF) to Bose glass (BG), and focus on the strong disorder regime where localization is driven by weak links. Based on high-precision density matrix renormalization group simulations, we numerically show that extreme local densities accurately capture the BKT transition, even for relatively short chains ranging from a few dozen to a hundred sites. We also discuss the SF-BG transition in the weak disorder regime, where finite-size effects pose greater challenges. Overall, our work seeks to establish a solid foundation for using extreme statistics of local observables, such as density, to probe delocalization-localization transitions in disordered quantum chains, both in the ground state and at high energy.

SAQ: Stabilizer-Aware Quantum Error Correction Decoder

Authors: David Zenati, Eliya Nachmani

arXiv ID: 2512.08914 | Date: 2025-12-09

Abstract: Quantum Error Correction (QEC) decoding faces a fundamental accuracy-efficiency tradeoff. Classical methods like Minimum Weight Perfect Matching (MWPM) exhibit variable performance across noise models and suffer from polynomial complexity, while tensor network decoders achieve high accuracy but at prohibitively high computational cost. Recent neural decoders reduce complexity but lack the accuracy needed to compete with computationally expensive classical methods. We introduce SAQ-Decoder, a unified framework combining transformer-based learning with constraint aware post-processing that achieves both near Maximum Likelihood (ML) accuracy and linear computational scalability with respect to the syndrome size. Our approach combines a dual-stream transformer architecture that processes syndromes and logical information with asymmetric attention patterns, and a novel differentiable logical loss that directly optimizes Logical Error Rates (LER) through smooth approximations over finite fields. SAQ-Decoder achieves near-optimal performance, with error thresholds of 10.99% (independent noise) and 18.6% (depolarizing noise) on toric codes that approach the ML bounds of 11.0% and 18.9% while outperforming existing neural and classical baselines in accuracy, complexity, and parameter efficiency. Our findings establish that learned decoders can simultaneously achieve competitive decoding accuracy and computational efficiency, addressing key requirements for practical fault-tolerant quantum computing systems.

Dominant Excitonic Superconductivity in a Three-component Hubbard Chain

Authors: Sheng Chen, Qiao Yang, Wéi Wú, Fadi Sun

arXiv ID: 2512.08784 | Date: 2025-12-09

Abstract: Understanding superconductivity emerging from repulsive fermions remains a major challenge in condensed matter physics. In this paper, we investigate the pairing tendencies in a one-dimensional, three component repulsive Hubbard model, using the density matrix renormalization group method. At half-filling, the system exhibits density wave ground state due to strong Hubbard repulsions. Upon doping, we find that Cooper pairs can emerge, whose fluctuations predominate the long-range physics in the system across a wide parameter range. The effective attractions between Cooper pairs are mediated by the particle-hole fluctuations in the third non-pairing component, resembling an excitonic mechanism of superconductivity. The coexistence of multiple density waves and superconductivity at different fermion fillings is explored. We also present an analytical study of the pairing mechanism in both weak and strong coupling limits. Our results provide a new perspective for understanding and exploring unconventional superconductivities in strongly correlated fermionic systems.

Triangular J1J_1-J2J_2 Heisenberg Antiferromagnet in a Magnetic Field

Authors: Thomas Bader, Shi Feng, Sasank Budaraju, Federico Becca, Johannes Knolle, Frank Pollmann

arXiv ID: 2512.08768 | Date: 2025-12-09

Abstract: The behavior of the paradigmatic J1J2J_1-J_2 triangular lattice Heisenberg antiferromagnet in a magnetic field remains unsettled despite decades of study. We map out the phase diagram using three complementary approaches, including self-consistent nonlinear spin-wave theory, density-matrix renormalization group, and variational Monte Carlo. This combined analysis resolves the competition among different field-induced magnetic orders and magnetization plateaux across the classically frustrated parameter range. In particular, there is a finite range in the parameter regime around J2/J1=18J_2/J_1=\frac{1}{8} in which i) upon the application of the external field, the gapless quantum spin liquid acquires a finite density of monopoles, and ii) by further increasing the field, two plateaux are clearly obtained at m=13m=\frac{1}{3} and m=12m=\frac{1}{2}. We discuss the experimental importance of the consecutive magnetization plateaux transitions as a signature of an underlying quantum spin-liquid phase.

Non-abelian quantum double models from iterated gauging

Authors: David Blanik, José Garre-Rubio

arXiv ID: 2512.08749 | Date: 2025-12-09

Abstract: We reconstruct all (2+1)D quantum double models of finite groups from their boundary symmetries through the repeated application of a gauging procedure, extending the existing construction for abelian groups. We employ the recently proposed categorical gauging framework, based on matrix product operators (MPOs), to derive the appropriate gauging procedure for the RepG\mathsf{Rep}\, G symmetries appearing in our construction and give an explicit description of the dual emergent GG symmetry, which is our main technical contribution. Furthermore, we relate the possible gapped boundaries of the quantum double models to the quantum phases of the one-dimensional input state to the iterated gauging procedure. Finally, we propose a gauging procedure for 1-form RepG\mathsf{Rep}\, G symmetries on a two-dimensional lattice and use it to extend our results to the construction of (3+1)D quantum doubles models through the iterative gauging of (2+1)-dimensional symmetries.

Geometry-driven transitions in sparse long-range spin models with cold atoms

Authors: Alex Gunning, Aydin Deger, Sridevi Kuriyattil, Andrew J. Daley

arXiv ID: 2512.08709 | Date: 2025-12-09

Abstract: We explore the influence of geometry in the critical behavior of sparse long-range spin models. We examine a model with interactions that can be continuously tuned to induce distinct changes in the metric, topology, and dimensionality of the coupling graph. This underlying geometry acts as the driver of criticality, with structural changes in the graph coinciding with and dictating the phase boundaries. We further discuss how this framework connects naturally to realizations in tweezer arrays with Rydberg excitations. In certain cases, the effective geometry can be incorporated in the layout of atoms in tweezers to realize phase transitions that preserve universal features, simplifying their implementation in near-term experiments.

Quantum simulation in the entanglement picture

Authors: D. -S. Wang, X. Xu, Y. -D. Liu

arXiv ID: 2512.08565 | Date: 2025-12-09

Abstract: The notion of ``picture'' is fundamental in quantum mechanics. In this work, a new picture, which we call entanglement picture, is proposed based on the novel channel-state duality, whose importance is revealed in quantum information science. We illustrate the application of entanglement picture in quantum algorithms for the simulation of many-body dynamics, quantum field theory, thermal physics, and more generic quantities.

Decay of spin helices in XXZ quantum spin chains with single-ion anisotropy

Authors: Florian Lange, Frank Göhmann, Gerhard Wellein, Holger Fehske

arXiv ID: 2512.08421 | Date: 2025-12-09

Abstract: Long-lived spin-helix states facilitate the study of non-equilibrium dynamics in quantum magnets. We consider the decay of transverse spin-helices in antiferromagnetic spin-SS XXZ chains with single-ion anisostropy. The spin-helix decay is observable in the time evolution of the local magnetization that we calculate numerically for the system in the thermodynamic limit using infinite time-evolving block decimation simulations. Although the single-ion anisotropy prevents helix states from being eigenstates of the Hamiltonian, they still can be long-lived for appropriately chosen wave numbers. In case of an easy-axis exchange anisotropy the single-ion anisotropy may even stabilize the helices. Within a spin-wave approximation, we obtain a condition giving an estimate for the most stable wave number QQ that agrees qualitatively with our numerical results.

Measurement-and Feedback-Driven Non-Equilibrium Phase Transitions on a Quantum Processor

Authors: Zhiyi Wu, Xuandong Sun, Songlei Wang, Jiawei Zhang, Xiaohan Yang, Ji Chu, Jingjing Niu, Youpeng Zhong, Xiao Chen, Zhi-Cheng Yang, Dapeng Yu

arXiv ID: 2512.07966 | Date: 2025-12-08

Abstract: Mid-circuit measurements and feedback operations conditioned on the measurement outcomes are essential for implementing quantum error-correction on quantum hardware. When integrated in quantum many-body dynamics, they can give rise to novel non-equilibrium phase transitions both at the level of each individual quantum trajectory and the averaged quantum channel. Experimentally resolving both transitions on realistic devices has been challenging due to limitations on the fidelity and the significant latency for performing mid-circuit measurements and feedback operations in real time. Here, we develop a superconducting quantum processor that enables global mid-circuit measurement with an average quantum non-demolition (QND) fidelity of 98.7% and fast conditional feedback with a 200 ns real-time decision latency. Using this platform, we demonstrate the coexistence of an absorbing-state transition in the quantum channel and a measurement-induced entanglement transition at the level of individual quantum trajectories. For the absorbing-state transition, we experimentally extract a set of critical exponents at the transition point, which is in excellent agreement with the directed percolation universality class. Crucially, the two transitions occur at distinct values of the tuning parameter. Our results demonstrate that adaptive quantum circuits provide a powerful platform for exploring non-equilibrium quantum many-body dynamics.

Performance Benchmarking of Tensor Trains for accelerated Quantum-Inspired Homogenization on TPU, GPU and CPU architectures

Authors: Sascha H. Hauck, Matthias Kabel, Nicolas R. Gauger

arXiv ID: 2512.07811 | Date: 2025-12-08

Abstract: Recent advances in high-resolution CT-imaging technology are creating a new class of ultra-high resolved micro-structural datasets that challenge the limits of traditional homogenization approaches. While state-of-the-art FFT-based homogenization techniques remain effective for moderate datasets, their memory footprint and computational cost grow rapidly with increasing resolution, making them increasingly inefficient for industrial-scale problems. To address these challenges, the recently developed Superfast-Fourier Transform (SFFT)-based homogenization algorithm leverages the memory-efficient low-rank representations of Tensor Trains (TTs), which reduce the storage and computational requirements of large-scale homogenization problems. Developed for CPU usage, SFFT-based Homogenization efficiently handles high-resolution datasets, assuming the underlying data is well-behaved. In this work, we investigate the performance of fundamental TT operations on modern hardware accelerators using the JAX framework. This benchmarking study, comparing CPUs, GPUs, and TPUs, evaluates execution times and computational efficiency. Building on these insights, we adapt the SFFT-based homogenization algorithm for usage on accelerators, achieving speed-ups of up to 10x relative to the CPU implementation, thus paving the road for the treatment of previously infeasible dataset sizes. Our results show that GPUs and TPUs achieve comparable performance in realistic scenarios, despite the relative immaturity of the TPU ecosystem, demonstrating the potential of both architectures to accelerate quantum-inspired techniques for industrial-scale simulations, particularly for homogenization problems.

Environment-matrix-product operator for boundary-free large-scale quantum many-body simulations

Authors: Souta Shimozono, Chisa Hotta

arXiv ID: 2512.07923 | Date: 2025-12-08

Abstract: We propose an alternative to the infinite density-matrix renormalization approach for accessing quantum many-body states within a finite-size calculation that faithfully mimics the thermodynamic limit. Our method constructs environment matrix product operators (MPOs) representing the Hamiltonian of semi-infinite regions surrounding the target system. Starting from the finite-size ground-state MPS, we contract its Hamiltonian representation to generate effective environment MPOs, which are then attached to a renewed finite system in a recursive manner. This iterative embedding drives the system toward a bulk-like state with negligible finite-size effects. The scheme requires no assumption of homogeneity and achieves unprecedentedly long real-time dynamics free from boundary reflections.

Tensor Network Fluid Simulations in Structured Domains Using the Lattice Boltzmann Method

Authors: Lukas Gross, Elie Mounzer, David M. Wawrzyniak, Josef M. Winter, Nikolaus A. Adams

arXiv ID: 2512.07615 | Date: 2025-12-08

Abstract: High-fidelity fluid simulations are central to understanding transport phenomena, yet resolving large or geometrically complex systems remains computationally prohibitive with existing methods. Recently, methods based on tensor-networks, commonly known as a quantum-inspired approach, were proposed to efficiently simulate flow in simple domains, where complexity emerges mostly from turbulence. Here, we substantially extend the understanding of such methods by demonstrating for the first time that also flows governed by translational or approximate symmetries of the geometry exhibit very low effective complexity in matrix product state (MPS) form. To this end, we introduce a tensor-network formulation of the lattice Boltzmann method based on MPS and demonstrate the generality of the method on three-dimensional flows through structured media and complex vascular geometries, establishing that tensor-network techniques can efficiently resolve fluid dynamics in complex domains previously inaccessible to MPS approaches. We show that in structured media, MPS representation yields compression ratios exceeding two orders of magnitude while preserving physical structure and dynamical fidelity. This reduction enables systematic numerical exploration of regimes that were previously intractable. Our results position tensor networks as a scalable paradigm for continuum mechanics.

Local Reversibility and Divergent Markov Length in 1+1-D Directed Percolation

Authors: Yu-Hsueh Chen, Tarun Grover

arXiv ID: 2512.07220 | Date: 2025-12-08

Abstract: Recent progress in open many-body quantum systems has highlighted the importance of the Markov length, the characteristic scale over which conditional correlations decay. It has been proposed that non-equilibrium phases of matter can be defined as equivalence classes of states connected by short-time evolution while maintaining a finite Markov length, a notion called local reversibility. A natural question is whether well-known classical models of non-equilibrium criticality fit within this framework. Here we investigate the Domany--Kinzel model -- which exhibits an active phase and an absorbing phase separated by a 1+1-D directed-percolation transition -- from this information-theoretic perspective. Using tensor network simulations, we provide evidence for local reversibility within the active phase. Notably, the Markov length diverges upon approaching the critical point, unlike classical equilibrium transitions where Markov length is zero due to their Gibbs character. Correspondingly, the conditional mutual information exhibits scaling consistent with directed percolation universality. Further, we analytically study the case of 1+1-D compact directed percolation, where the Markov length diverges throughout the phase diagram due to spontaneous breaking of domain-wall parity symmetry from strong to weak. Nevertheless, the conditional mutual information continues to faithfully detect the corresponding phase transition.

Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties

Authors: Viktoriia Borovik, Hannah Friedman, Serkan Hoşten, Max Pfeffer

arXiv ID: 2512.06939 | Date: 2025-12-07

Abstract: We study energy minimization problems in quantum chemistry through the lens of computational algebraic geometry. We focus on minimizing the Rayleigh quotient of a Hamiltonian over a tensor train variety. The complex critical points of this problem approximate eigenstates of the quantum system, with the global minimum approximating the ground state. We call the number of critical points the Rayleigh-Ritz degree. After introducing tensor train varieties, we identify instances when they are Segre products of projective spaces. We also report what we know about the defining ideals of tensor trains. We present a birational parametrization of them from products of Grassmannians. Along the way, we study the Rayleigh-Ritz degree, and we introduce the Rayleigh-Ritz discriminant, which describes Hamiltonians that lead to deficient number of critical points. We use homotopy continuation to compute all critical points of this optimization problem over various tensor train and determinantal varieties. Finally, we use these results to benchmark state-of-the-art methods, the Alternating Linear Scheme and Density Matrix Renormalization Group.

Maximum Independent Set via Probabilistic and Quantum Cellular Automata

Authors: Federico Dell'Anna, Matteo Grotti, Vito Giardinelli

arXiv ID: 2512.06778 | Date: 2025-12-07

Abstract: We study probabilistic cellular automata (PCA) and quantum cellular automata (QCA) as frameworks for solving the Maximum Independent Set (MIS) problem. We first introduce a synchronous PCA whose dynamics drives the system toward the manifold of maximal independent sets. Numerical evidence shows that the MIS convergence probability increases significantly as the activation probability p tends to 1, and we characterize how the steps required to reach the absorbing state scale with system size and graph connectivity. Motivated by this behavior, we construct a QCA combining a pure dissipative phase with a constraint-preserving unitary evolution that redistributes probability within this manifold. Tensor Network simulations reveal that repeated dissipative--unitary cycles concentrate population on MIS configurations. We also provide an empirical estimate of how the convergence time scales with graph size, suggesting that QCA dynamics can provide an efficient alternative to adiabatic and variational quantum optimization methods based exclusively on local and translationally invariant rules.

Quantum Mpemba effect in long-ranged U(1)-symmetric random circuits

Authors: Han-Ze Li, Ching Hua Lee, Shuo Liu, Shi-Xin Zhang, Jian-Xin Zhong

arXiv ID: 2512.06775 | Date: 2025-12-07

Abstract: The Mpemba effect, where a state prepared farther from equilibrium relaxes faster to equilibrium than one prepared closer, has a quantum counterpart where relaxation is resolved by conserved charge. However, the fate of the quantum Mpemba effect in systems with long-range interactions remains an open question. Here, we study the quantum Mpemba effect in long-ranged, U(1)-symmetric random unitary circuits. Using annealed Rényi-2 entanglement asymmetry computed via replica tensor networks and exact diagonalization, we track the symmetry restoration from three types of tilted product states: ferromagnetic, antiferromagnetic, and ferromagnetic with a central domain wall. The quantum Mpemba effect is present for tilted ferromagnetic states at all interaction ranges, but absent for tilted antiferromagnetic states, and occurs for the domain-wall state only in effectively short-ranged circuits, where the Mpemba time tMt_{\rm M} is found to scale with the subsystem size NAN_A as tM ⁣ ⁣NAzt_{\rm M}\!\sim\!N_{A}^{\,z}, with the dynamical exponent z=min(α1,2)z=\min(α-1,2). These results reveal how the quantum Mpemba effect is governed by the interplay between interaction range and initial-state charge bias in long-ranged chaotic systems.

Real-Time Dynamics in Two Dimensions with Tensor Network States via Time-Dependent Variational Monte Carlo

Authors: Yantao Wu

arXiv ID: 2512.06768 | Date: 2025-12-07

Abstract: Reliably simulating two-dimensional many-body quantum dynamics with projected entangled pair states (PEPS) has long been a difficult challenge. In this work, we overcome this barrier for low-energy quantum dynamics by developing a stable and efficient time-dependent variational Monte Carlo (tVMC) framework for PEPS. By analytically removing all gauge redundancies of the PEPS manifold and exploiting tensor locality, we obtain a numerically well-conditioned stochastic reconfiguration (SR) equation amenable to robust solution using the efficient Cholesky decomposition, enabling long-time evolution in previously inaccessible regimes. We demonstrate the power and generality of the method through four representative real-time problems in two dimensions: (I) chiral edge propagation in a free-fermion Chern insulator; (II) fractionalized charge transport in a fractional Chern insulator; (III) vison confinement dynamics in the Higgs phase of a Z2 lattice gauge theory; and (IV) superfluidity and critical velocity in interacting bosons. All simulations are performed on 12x12 or 13x13 lattices with evolution times T = 10 to 12 using modest computational resources (1 to 5 days on a single GPU card). Where exact benchmarks exist (case I), PEPS-tVMC matches free-fermion dynamics with high accuracy up to T = 12. These results establish PEPS-tVMC as a practical and versatile tool for real-time quantum dynamics in two dimensions. The method extends the reach of classical tensor-network simulations for studying elementary excitations in quantum many-body systems and provides a valuable computational counterpart to emerging quantum simulators.

Exploring electron spin dynamics in spin chains using defects as a quantum probe

Authors: L. Soriano, A. Manoj-Kumar, G. Gerbaud, A. Savoyant, R. Dassonneville, H. Vezin, O. Jeannin, M. Orio, M. Fourmigué, S. Bertaina

arXiv ID: 2512.06722 | Date: 2025-12-07

Abstract: We investigate the quantum dynamics of the electron spin resonance of topological defects (edge state) in dimerized chains. These objects are discontinuities of the spin chain protected by the properties of the global system leading to a quantum many-body multiplet protected from the environment decoherence. Despite recent achievements in the realization of isolated and finite spin chains, the potential implementation in quantum devices needs the knowledge of the relaxation and decoherence sources. Our study reveals that electron spin lattice relaxation is governed at lowest temperatures by phonon-bottlenecked process and at high temperature by the chain dimerization gap. We show that the inter edge-state effective dipolar field is reduced by the intrachain exchange coupling leading to a longer coherence time than isolated ions at equivalent concentration. Ultimately, we demonstrate that the homogeneous broadening is governed by the intra-chain dipolar field, and we establish design principles for optimizing coherence in future materials.

Spurious Strange Correlators in Symmetry-Protected Topological Phases

Authors: Wei-Liang Gao, Jie-Yu Zhang, Zheng-Xin Liu, Peng Ye

arXiv ID: 2512.06691 | Date: 2025-12-07

Abstract: Strange correlator is a powerful tool widely used in detecting symmetry-protected topological (SPT) phases. However, the result of strange correlator crucially relies on the adoption of the reference state. In this work, we report that an ill-chosen reference state can induce spurious long-range strange correlators in trivial SPT phases, leading to false positives in SPT diagnosis. Using matrix product state (MPS) representation, we trace the origin of these spurious signals in trivial SPT phases to the magnitude-degeneracy of the transfer matrix. We systematically classify three distinct mechanisms responsible for such degeneracy, each substantiated by concrete examples: (1) the presence of high-dimensional irreducible representations in the entanglement space; (2) a phase mismatch in symmetry representations between the target and reference states; and (3) long-range order arising from symmetry breaking. Our findings clarify the importance of the choice of proper reference states, providing a guideline to avoid pitfalls and correctly identify SPT order using strange correlators.

Kitaev Meets AKLT: Competing Quantum Disorder in Spin-3/2 Honeycomb Systems

Authors: Sogen Ikegami, Kiyu Fukui, Rico Pohle, Yukitoshi Motome

arXiv ID: 2512.06322 | Date: 2025-12-06

Abstract: We investigate an S=3/2 quantum spin model on a two-dimensional honeycomb lattice that continuously interpolates between two paradigmatic quantum disordered states with distinct entanglement structures: the Kitaev quantum spin liquid and the Affleck-Kennedy-Lieb-Tasaki (AKLT) valence bond solid. Combining classical, semi-classical, and exact diagonalization approaches, we map out the ground-state phase diagram and elucidate the role of quantum fluctuations across the entire parameter range. While classical and semi-classical frameworks predict noncoplanar orders competing with a collinear Néel state, we find these phases to be fragile: once full quantum fluctuations are included, they melt into a quantum-entangled state characterized by suppressed spin correlations and enhanced entanglement entropy. Our findings highlight how competition between qualitatively different quantum disordered phases provides a fertile playground for unconventional phases emerging from their interplay and quantum fluctuations.

A "negative" route to pair density wave order

Authors: Hao-Xin Wang, Yi-Jian Hu, Wen Huang, Hong Yao

arXiv ID: 2512.06100 | Date: 2025-12-05

Abstract: Pair density waves (PDW) are novel forms of superconducting states that exhibit periodically modulated pairing. A remaining challenge is to elucidate how intrinsic PDW order can emerge robustly in strongly correlated electrons. Here we propose that PDW is prone to form in strongly coupled multiband superconductors simply with interband Cooper pairing between electrons from oppositely dispersing bands. This scenario is heuristically motivated by the observation that uniform interband pairing in such systems would exhibit negative superfluid weight -- a signature of an instability towards pairing modulation, implying that PDW emerges naturally in the true ground state. Using large-scale density-matrix-renormalization-group calculations with finite-size scaling analysis, we demonstrate this PDW mechanism in a minimal model with strong interband attractions. Our simulations reveal power-law superconducting correlations characterized by incommensurate modulations. The exponent KscK_{sc} of the power-law PDW correlation decreases systematically with increasing ladder width, confirming a genuine long-range PDW order in the 2D limit. Our study therefore demonstrates a promising route to robust PDW states in multiband systems.

Interplay of Rashba and Dresselhaus Spin-Orbit Couplings on the Stability of Topological FFLO Phases in 1D Fermi Gases

Authors: Hamid Mosadeq, Mohammad-Hossein Zare, Reza Asgari

arXiv ID: 2512.05901 | Date: 2025-12-05

Abstract: We investigate the stabilization of topological Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phases, with a specific emphasis on the intraband FFLO phase, in a one-dimensional (1D) Fermi gas subjected to an external magnetic field. This research highlights the crucial role of the interplay between Rashba spin-orbit coupling (RSOC) and Dresselhaus spin-orbit coupling (DSOC). Employing a Fermi-Hubbard model alongside the density matrix renormalization group (DMRG) method, we examine the combined effects of RSOC and DSOC on these exotic superfluid phases, taking into account attractive fermionic interactions. Our principal finding reveals that while RSOC primarily stabilizes conventional zero-momentum pairing, DSOC performs a distinct and crucial role in selectively stabilizing the intraband FFLO phase. This stabilization is achieved by enhancing spin polarization within a single helicity band and suppressing interband coherence, thereby facilitating the formation of finite-momentum FFLO pairs within the same band and resulting in the emergence of a topologically nontrivial superfluid. This targeted control of intraband FFLO pairing paves the way for new strategies in the manipulation of superfluid phases in spin-orbit coupled systems and offers essential insights for experimental realizations in ultracold atomic gases, with implications for topological quantum computing and Majorana fermions.

Lattice field theory for superconducting circuits

Authors: Joshua Lin, Max Hays, Stephen Sorokanich, Julian Bender, Phiala E. Shanahan, Neill C. Warrington

arXiv ID: 2512.05851 | Date: 2025-12-05

Abstract: Large superconducting quantum circuits have a number of important applications in quantum computing. Accurately predicting the performance of these devices from first principles is challenging, as it requires solving the many-body Schrödinger equation. This work introduces a new, general ab-initio method for analyzing large quantum circuits based on lattice field theory, a tool commonly applied in nuclear and particle physics. This method is competitive with state-of-the-art techniques such as tensor networks, but avoids introducing systematic errors due to truncation of the infinite-dimensional Hilbert space associated with superconducting phases. The approach is applied to fluxonium, a specific many-component superconducting qubit with favorable qualities for quantum computation. A systematic study of the influence of impedance on fluxonium is conducted that parallels previous experimental studies, and ground capacitance effects are explored. The qubit frequency and charge noise dephasing rate are extracted from statistical analyses of charge noise, where thousands of instantiations of charge disorder in the Josephson junction array of a fixed fluxonium qubit are explicitly averaged over at the microscopic level. This is difficult to achieve with any other existing method.

Investigating a Quantum-Inspired Method for Quantum Dynamics

Authors: Bo Xiao, Benedikt Kloss, E. Miles Stoudenmire

arXiv ID: 2512.05185 | Date: 2025-12-04

Abstract: Building on recent advances in quantum algorithms which measure and reuse qubits and in efficient classical simulation leveraging projective measurements, we extend these frameworks to real-time dynamics of quantum many-body systems undergoing discrete-time and continuous-time Hamiltonian evolution, and find improvements that significantly reduce sampling overhead. The approach exploits causal light-cone structure by interleaving time and space evolution and applying projective measurements as soon as local subsystems reach the target physical time, suppressing entanglement growth. Comparing to time-evolving block decimation, the method reaches longer times per sample for the same resources. We also gain the ability to study dynamics of entanglement that would be occurring on quantum hardware when following similar protocols, such as the holographic quantum dynamics simulation framework. We show how to efficiently obtain local observables as well as equal-time and time-dependent correlation functions. Our findings show how optimizations for quantum hardware can benefit classical tensor network simulations and how such classical methods can yield insights into the utility of quantum simulations.

Quantum compilation framework for data loading

Authors: Guillermo Alonso-Linaje, Utkarsh Azad, Jay Soni, Jarrett Smalley, Leigh Lapworth, Juan Miguel Arrazola

arXiv ID: 2512.05183 | Date: 2025-12-04

Abstract: Efficient encoding of classical data into quantum circuits is a critical challenge that directly impacts the scalability of quantum algorithms. In this work, we present an automated compilation framework for resource-aware quantum data loading tailored to a given input vector and target error tolerance. By explicitly exploiting the trade-off between exact and approximate state preparation, our approach systematically partitions the total error budget between precision and approximation errors, thereby minimizing quantum resource costs. The framework supports a comprehensive suite of state-of-the-art methods, including multiplexer-based loaders, quantum read-only memory (QROM) constructions, sparse encodings, matrix product states (MPS), Fourier series loaders (FSL), and Walsh transform-based diagonal operators. We demonstrate the effectiveness of our framework across several applications, where it consistently uncovers non-obvious, resource-efficient strategies enabled by controlled approximation. In particular, we analyze a computational fluid dynamics workflow where the automated selection of MPS state preparation and Walsh transform-based encoding, combined with a novel Walsh-based measurement technique, leads to resource reductions of over four orders of magnitude compared to previous approaches. We also introduce two independent advances developed through the framework: a more efficient circuit for d-diagonal matrices, and an optimized block encoding for kinetic energy operators. Our results underscore the indispensable role of automated, approximation-aware compilation in making large-scale quantum algorithms feasible on resource-constrained hardware.

Maestro: Intelligent Execution for Quantum Circuit Simulation

Authors: Oriol Bertomeu, Hamzah Ghayas, Adrian Roman, Stephen DiAdamo

arXiv ID: 2512.04216 | Date: 2025-12-03

Abstract: Quantum circuit simulation remains essential for developing and validating quantum algorithms, especially as current quantum hardware is limited in scale and quality. However, the growing diversity of simulation methods and software tools creates a high barrier to selecting the most suitable backend for a given circuit. We introduce Maestro, a unified interface for quantum circuit simulation that integrates multiple simulation paradigms - state vector, MPS, tensor network, stabilizer, GPU-accelerated, and p-block methods - under a single API. Maestro includes a predictive runtime model that automatically selects the optimal simulator based on circuit structure and available hardware, and applies backend-specific optimizations such as multiprocessing, GPU execution, and improved sampling. Benchmarks across heterogeneous workloads demonstrate that Maestro outperforms individual simulators in both single-circuit and large batched settings, particularly in high-performance computing environments. Maestro provides a scalable, extensible platform for quantum algorithm research, hybrid quantum-classical workflows, and emerging distributed quantum computing architectures.

2D Helical Twist Controls Tricritical Point in an Interacting Majorana Chain

Authors: Hekai Zhao, Philip Phillips

arXiv ID: 2512.04180 | Date: 2025-12-03

Abstract: We analyze a series of interacting Majorana Fermion chains with finite range pair interactions with coupling strength gg that all exhibit a tri-critical point that separates an Ising critical phase from a supersymmetric gapped phase. We first notice that the interacting models exhibit an even-odd asymmetry depending on the number of sites, δδ, over which the interaction ranges. The even case exhibits competing order, thereby making it numerically untractable while the odd case exhibits an exactly solvable point at g=0.5g=-0.5 where the entanglement entropy vanishes. By introducing a swirling geometrical twist, we map our 1D δδ-range chains to a series of 2D δ/2δ/2-width models. Our new 2D models possess a unique helical boundary condition, constructed from 1D chains with the end of one connected to the start of another. We propose that the phase transition in the 1D system can be understood as a finite-system size transition in 2D. That is, the gcδg_c-δ behavior is controlled by a 2D tri-critical universality class at δδ\to\infty limit and is predicted by finite-size scaling theory.

Tensor renormalization group calculations of partition-function ratios

Authors: Satoshi Morita, Naoki Kawashima

arXiv ID: 2512.03395 | Date: 2025-12-03

Abstract: The behavior of dimensionless quantities defined as ratios of partition functions is analyzed to investigate phase transitions and critical phenomena. At criticality, the universal values of these ratios can be predicted from conformal field theory (CFT) through the modular-invariant partition functions on a torus. We perform numerical calculations using the bond-weighted tensor renormalization group for three two-dimensional models belonging to different universality classes: the Ising model, the three-state Potts model, and the four-state Potts model. The partition-function ratios obey the same finite-size scaling form as the Binder parameter, and their critical values agree well with the universal values predicted by CFT. In the four-state Potts model, we observe logarithmic corrections in the system-size dependence of these ratios.

Sketch Tomography: Hybridizing Classical Shadow and Matrix Product State

Authors: Xun Tang, Haoxuan Chen, Yuehaw Khoo, Lexing Ying

arXiv ID: 2512.03333 | Date: 2025-12-03

Abstract: We introduce Sketch Tomography, an efficient procedure for quantum state tomography based on the classical shadow protocol used for quantum observable estimations. The procedure applies to the case where the ground truth quantum state is a matrix product state (MPS). The density matrix of the ground truth state admits a tensor train ansatz as a result of the MPS assumption, and we estimate the tensor components of the ansatz through a series of observable estimations, thus outputting an approximation of the density matrix. The procedure is provably convergent with a sample complexity that scales quadratically in the system size. We conduct extensive numerical experiments to show that the procedure outputs an accurate approximation to the quantum state. For observable estimation tasks involving moderately large subsystems, we show that our procedure gives rise to a more accurate estimation than the classical shadow protocol. We also show that sketch tomography is more accurate in observable estimation than quantum states trained from the maximum likelihood estimation formulation.

Magic of the Well: assessing quantum resources of fluid dynamics data

Authors: Antonio Francesco Mello, Mario Collura, E. Miles Stoudenmire, Ryan Levy

arXiv ID: 2512.03177 | Date: 2025-12-02

Abstract: We investigate the quantum resource requirements of a dataset generated from simulations of two-dimensional, periodic, incompressible shear flow, aimed at training machine learning models. By measuring entanglement and non-stabilizerness on MPS-encoded functions, we estimate the computational complexity encountered by a stabilizer or a tensor network solver applied to Computational Fluid Dynamics (CFD) simulations across different flow regimes. Our analysis reveals that, under specific initial conditions, the shear width identifies a transition between resource-efficient and resource-intensive regimes for non-trivial evolution. Furthermore, we find that the two resources qualitatively track each other in time, and that the mesh resolution along with the sign structure play a crucial role in determining the resource content of the encoded state. These findings offer useful guidelines for the development of scalable, quantum-inspired approaches to fluid dynamics.

Entanglement evolution from entangled multipodal states

Authors: Konstantinos Chalas, Pasquale Calabrese, Colin Rylands

arXiv ID: 2512.03032 | Date: 2025-12-02

Abstract: In a periodic lattice system an entangled antipodal pair state, otherwise known as a crosscap state, is a simple two site product state in which spins at antipodal sites are prepared in Bell pairs. Such states have maximal bipartite entanglement and serve as a useful platform for studying the quench dynamics of systems which have large initial entanglement. In this paper, we study a generalization of these states which we dub entangled mutipodal states. These states, which are defined for fermionic systems, generalize the crosscap states by having correlations among more than two sites, specifically, those which sit at the vertices of regular polygons. By construction, the states are Gaussian and translationally invariant allowing many of their properties to be understood. We study the bipartite entanglement entropy of these states both in and out of equilibrium. In equilibrium, the entanglement profile as a function of subsystem size exhibits two distinct regimes, a volume-law growth followed by a saturation to a constant value, thus generalizing the Page-curve profile of the crosscap state. In the non-equilibrium setting, we study quenches from these initial states to the free-fermion chain, whose ensuing dynamics displays a far richer structure compared to the crosscap case. We interpret our results in terms of the quasiparticle picture, which requires multiplets of quasiparticles to be excited non-locally around the system. This scenario is confirmed by the appearance of a post-quench, negative tripartite information.

Information dynamics and symmetry breaking in generic monitored Z2\mathbb{Z}_2-symmetric open quantum systems

Authors: Jacob Hauser, Ali Lavasani, Sagar Vijay, Matthew P. A. Fisher

arXiv ID: 2512.03031 | Date: 2025-12-02

Abstract: We investigate the steady-state phases of generic Z2\mathbb{Z}_2-symmetric monitored, open quantum dynamics. We describe the phases systematically in terms of both information-theoretic diagnostics and spontaneous breaking of strong and weak symmetries of the dynamics. We find a completely broken phase where information is retained by the quantum system, a strong-to-weak broken phase where information is leaked to the environment, and an unbroken phase where information is learned by the observer. We find that weak measurement and dephasing alone constitute a minimal model for generic open systems with Z2\mathbb{Z}_2 symmetry, but we also explore perturbations by unitary gates. For a 1d set of qubits, we examine information-theoretic and symmetry-breaking observables in the path integral of the doubled state. This path integral reduces to the standard classical 2d random-bond Ising model in certain limits but generically involves negative weights, enabling a special self-dual random-bond Ising model at the critical point when only measurements are present. We obtain numerical evidence for the steady-state phases using efficient tensor network simulations of the doubled state.

Lectures on Quantum Field Theory on a Quantum Computer

Authors: Aninda Sinha, Ujjwal Basumatary

arXiv ID: 2512.02706 | Date: 2025-12-02

Abstract: The lecture notes cover the basics of quantum computing methods for quantum field theory applications. No detailed knowledge of either quantum computing or quantum field theory is assumed and we have attempted to keep the material at a pedagogical level. We review the anharmonic oscillator, using which we develop a hands-on treatment of certain interesting QFTs in 1+1D1+1D: φ4φ^4 theory, Ising field theory, and the Schwinger model. We review quantum computing essentials as well as tensor network techniques. The latter form an essential part for quantum computing benchmarking. Some error modelling on QISKIT is also done in the hope of anticipating runs on NISQ devices. These lecture notes are the expanded version of a one semester course taught by AS during August-November 2025 at the Indian Institute of Science and TA-ed by UB. The programs written for this course are available in a GitHub repository.

Efficient Simulation of the 2D Hubbard Model via Hilbert Space-Filling Curve Mapping

Authors: Ashkan Abedi, Vittorio Giovannetti, Dario De Santis

arXiv ID: 2512.02666 | Date: 2025-12-02

Abstract: We investigate tensor network simulations of the two-dimensional Hubbard model by mapping the lattice onto a one-dimensional chain using space-filling curves. In particular, we focus on the Hilbert curve, whose locality-preserving structure minimizes the range of effective interactions in the mapped model. This enables a more compact matrix product state (MPS) representation compared to conventional snake mapping. Through systematic benchmarks, we show that the Hilbert curve consistently yields lower ground-state energies at fixed bond dimension, with the advantage increasing for larger system sizes and in physically relevant interaction regimes. Our implementation reaches clusters up to 32×3232\times32 sites with open and periodic boundary conditions, delivering reliable ground-state energies and correlation functions in agreement with established results, but at significantly reduced computational cost. These findings establish space-filling curve mappings, particularly the Hilbert curve, as a powerful tool for extending tensor-network studies of strongly correlated two-dimensional quantum systems beyond the limits accessible with standard approaches.

Tensor Network Based Feature Learning Model

Authors: Albert Saiapin, Kim Batselier

arXiv ID: 2512.02547 | Date: 2025-12-02

Abstract: Many approximations were suggested to circumvent the cubic complexity of kernel-based algorithms, allowing their application to large-scale datasets. One strategy is to consider the primal formulation of the learning problem by mapping the data to a higher-dimensional space using tensor-product structured polynomial and Fourier features. The curse of dimensionality due to these tensor-product features was effectively solved by a tensor network reparameterization of the model parameters. However, another important aspect of model training - identifying optimal feature hyperparameters - has not been addressed and is typically handled using the standard cross-validation approach. In this paper, we introduce the Feature Learning (FL) model, which addresses this issue by representing tensor-product features as a learnable Canonical Polyadic Decomposition (CPD). By leveraging this CPD structure, we efficiently learn the hyperparameters associated with different features alongside the model parameters using an Alternating Least Squares (ALS) optimization method. We prove the effectiveness of the FL model through experiments on real data of various dimensionality and scale. The results show that the FL model can be consistently trained 3-5 times faster than and have the prediction quality on par with a standard cross-validated model.

Laplace Approximation For Tensor Train Kernel Machines In System Identification

Authors: Albert Saiapin, Kim Batselier

arXiv ID: 2512.02532 | Date: 2025-12-02

Abstract: To address the scalability limitations of Gaussian process (GP) regression, several approximation techniques have been proposed. One such method is based on tensor networks, which utilizes an exponential number of basis functions without incurring exponential computational cost. However, extending this model to a fully probabilistic formulation introduces several design challenges. In particular, for tensor train (TT) models, it is unclear which TT-core should be treated in a Bayesian manner. We introduce a Bayesian tensor train kernel machine that applies Laplace approximation to estimate the posterior distribution over a selected TT-core and employs variational inference (VI) for precision hyperparameters. Experiments show that core selection is largely independent of TT-ranks and feature structure, and that VI replaces cross-validation while offering up to 65x faster training. The method's effectiveness is demonstrated on an inverse dynamics problem.

Improved Ising Meson Spectroscopy Simulation on a Noisy Digital Quantum Device

Authors: Hao-Ti Hung, Isabel Nha Minh Le, Johannes Knolle, Ying-Jer Kao

arXiv ID: 2512.02516 | Date: 2025-12-02

Abstract: The transverse-field Ising model serves as a paradigm for studying confinement and excitation spectra, particularly the emergence of E8E_8 symmetry near criticality. However, experimentally resolving the Ising meson spectroscopy required to verify these symmetries is challenging on near-term quantum hardware due to the depth of circuits required for real-time evolution. Here, we demonstrate improved spectroscopy of confined excitations using two distinct error-resilient circuit construction techniques on the IBM Torino device: first-order Trotter decomposition utilizing native fractional gates, and a tensor-network-based circuit compression via Riemannian optimization. By analyzing the Fourier spectrum of error-mitigated time-series data, we successfully identify key signatures of E8E_8 symmetry despite hardware noise. These results validate the viability of both circuit compression and hardware-efficient compilation for probing complex topological phenomena on NISQ devices.

Superchannel without Tears: A Generalized Occam's Razor for Quantum Processes

Authors: Yunlong Xiao

arXiv ID: 2512.02493 | Date: 2025-12-02

Abstract: Quantum channels function as the operational primitives of quantum theory, while superchannels describe the most general transformations acting upon them. Yet the prevailing framework for superchannels is both internally inconsistent, owing to the coexistence of distinct Choi operator constructions, and structurally incomplete, lacking the analogue of representations that ground channel theory. We resolve these issues by combining tensor-network methods with a generalized Occam's razor introduced here, establishing a unified foundation for superchannels. Our framework establishes the connections between competing Choi formulations, develops the Kraus, Stinespring, and Liouville representations for superchannels, and provides a simplified derivation of the realization theorem that identifies the minimal memory required to implement a given transformation. These structural tools also enable characterizations of superchannels that destroy quantum correlations or causal structure, opening a systematic route to non-Markovian quantum dynamics.

J1J2J_1-J_2 Triangular Lattice Antiferromagnet in a Magnetic Field

Authors: Anna Keselman, Xinyuan Xu, Hao Zhang, Cristian D. Batista, Oleg A. Starykh

arXiv ID: 2512.02150 | Date: 2025-12-01

Abstract: We investigate the spin-1/2 J1J2J_1-J_2 triangular-lattice Heisenberg antiferromagnet in a magnetic field by combining large-scale density matrix renormalization group (DMRG) simulations with self-consistent spin-wave theory. The resulting field-coupling phase diagram reveals that quantum fluctuations stabilize coplanar order across the entire parameter range, giving rise to a characteristic sequence of magnetization plateaux. Near the quantum-spin-liquid window 0.06J2/J10.140.06 \lesssim J_2/J_1 \lesssim 0.14, which extends to magnetic field BJ1B \sim J_1, we identify overlapping m=1/3m = 1/3 and m=1/2m = 1/2 plateaux - a distinctive hallmark of the system's proximity to the low-field spin-liquid regime. The excellent quantitative agreement between DMRG and self-consistent one-loop spin-wave calculations demonstrates that semiclassical approaches can reliably capture and parameterize the plateau phases of triangular quantum antiferromagnets.

Efficient Time Evolution of 2D Open-Quantum Lattice Models with Long-Range Interactions using Tensor Networks

Authors: Jack Dunham, Marzena H. Szymańska

arXiv ID: 2512.01781 | Date: 2025-12-01

Abstract: Simulating many-body open quantum systems is an extremely challenging problem, with methods often restricted to either models with nearest-neighbor interactions or semi-classical approximations. In particular, modeling two-dimensional systems with realistic long-range interactions, in addition to dissipation, is of vital importance to the development of modern quantum computing and simulation platforms. In this paper, we present a construction of the time-evolution operator, as a projected entangled pair operator (denoted tePEPO), that can be used to evolve a tensor network ansatz through time. Interactions beyond nearest-neighbor, including interactions between sites not collinear in the lattice, can be represented efficiently as a tePEPO. Furthermore, we obtain approximations to realistic radial long-range interactions decaying with a power-law, that give accurate results with small tePEPO bond dimension. Finally, we consider a physical example of a Rydberg atom Hamiltonian with long-range dipolar interactions, and show evidence of a dipole-dipole blockading effect in presence of dissipation. This work demonstrates the applicability of tensor networks to two-dimensional systems widely studied in experiments, but previously inaccessible to non-semi-classical methods.

Floquet-induced px+ipyp_x+ip_y bosonic pair condensate

Authors: Zhizhen Chen, Jiale Huang, Mingpu Qin, Zi Cai

arXiv ID: 2512.01674 | Date: 2025-12-01

Abstract: In this study, we propose a dynamical pairing mechanism other than the pair-wise interactions. Starting from a two-dimensional hard-core boson model with periodically modulated hopping amplitude, we derive an effective Floquet Hamiltonian with three-site interactions that are responsible for unconventional pairing between adjacent bosons. By performing a density matrix renormalization group study on this three-site interacting Hamiltonian, we reveal a bosonic pair condensate with px+ipyp_x+ ip_y symmetry, while the single-particle Bose-Einstein condensate is completely depleted. The experimental implementations of the proposed model on polar molecular systems and superconducting quantum circuit have also been discussed.

A Provably Efficient Method for Tensor Ring Decomposition and Its Applications

Authors: Han Chen, Sitan Chen, Anru R. Zhang

arXiv ID: 2512.01016 | Date: 2025-11-30

Abstract: We present the first deterministic, finite-step algorithm for exact tensor ring (TR) decomposition, addressing an open question about the existence of such procedures. Our method leverages blockwise simultaneous diagonalization to recover TR-cores from a limited number of tensor observations, providing both algebraic insight and practical efficiency. We extend the approach to the symmetric TR setting, where parameter complexity is significantly reduced and applications arise naturally in physics-based modeling and exchangeable data analysis. To handle noisy observations, we develop a robust recovery scheme that couples our initialization with alternating least squares, achieving faster convergence and improved accuracy compared to classic methods. As applications, we obtain new algorithms for questions in other domains where tensor ring decomposition is a key primitive, namely matrix product state tomography in quantum information, and provable learning of pushforward distributions in the foundations of machine learning. These contributions advance the algorithmic foundations of TR decomposition and open new opportunities for scalable tensor network computation.

Exact quantum dynamics of Fermi--Hubbard systems using the Gaussian phase-space representation with diffusion gauges

Authors: F Rousse, M Fasi, A Dmytryshyn, M Gulliksson, J F Corney, M Ogren

arXiv ID: 2512.00987 | Date: 2025-11-30

Abstract: We use the Gaussian Phase-Space Representation to solve the real-time dynamic of interacting fermions in 1D, 2D, and 3D systems. The method is exact up to a spiking point, which represents a limit on the practical simulation time. The spiking can be delayed, and the practical simulation time extended, by adjusting the gauges of the representation, resulting in different equivalent stochastic differential equations. Here, we work on the so-called diffusion gauge and propose an algorithm to find efficiently new implementations of the noise terms. Compared with our initial results [F. Rousse \textit{et al.} 2024, J. Phys. A: Math. Theor. \textbf{57}, 015303], the new method achieves a significantly longer practical simulation time and can be applied to significantly larger systems.

Scaling of a Mutual-Information Distance in One-dimensional Quantum Spin Chains

Authors: Beau Leighton-Trudel

arXiv ID: 2512.00649 | Date: 2025-11-29

Abstract: We introduce a geometric scaling relation that characterizes the local scale behavior of correlations using the informational distance dE=K0/Id_E = K_0/\sqrt{I}, where II is the mutual information. We define a geometric conversion factor, GrdEG \equiv \partial_r d_E, which quantifies the local scale. We show that GG relates directly to II via GIκG \propto I^κ. For systems with power-law correlations I(r)rXI(r) \sim r^{-X}, the metric scaling exponent is κ=1/X1/2κ= 1/X - 1/2. A key consequence is that the geometric scale GG is uniform (position-independent) if and only if κ=0κ= 0, which occurs precisely at X=2X = 2. This identifies X=2X = 2 as the unique condition for a uniform and metric informational distance. We validate this relation using DMRG simulations of the 1D XXZ chain and exact results for the XX model. We demonstrate two falsifiable diagnostics: (i) G(r)G(r) is flat in the bulk at criticality (X2X \approx 2) but varies strongly when gapped; (ii) a coordinate-agnostic slope test of logG\log G versus logI\log I at the XX benchmark (X=2X = 2) yields κ0κ\simeq 0. This approach provides a coordinate-independent method for identifying scaling regimes that helps to reduce ambiguity from non-universal amplitudes and from the fitting choices in standard power-law analyses, and defines a simple post-processing pipeline that can be applied directly to numerical or experimental mutual-information data.

A Heuristic for Matrix Product State Simulation of Out-of-Equilibrium Dynamics of Two-Dimensional Transverse-Field Ising Models

Authors: Salvatore Mandrà, Nikita Astrakhantsev, Sergei Isakov, Benjamin Villalonga, Brayden Ware, Tom Westerhout, Kostyantyn Kechedzhi

arXiv ID: 2511.23438 | Date: 2025-11-28

Abstract: Out-of-equilibrium dynamics of non-integrable Hamiltonian many-body quantum systems are characterized by highly entangled wave functions. Near-maximal entanglement arises in systems exhibiting thermalization or pre-thermalization, where the system converges to a steady state with a fixed energy density. Classical simulation of the time dependence of such wave functions requires exponential resources. However, typical computations aim to estimate expectation values of local operators and correlation functions to some expected precision. For thermalizing systems at sufficiently high energy densities, such computations do not require storing the full wave function. Nonetheless, constructing classical algorithms for intermediate energy densities has remained a challenge. In this paper, we propose a heuristic approach to accelerate the convergence of Matrix Product State (MPS) simulations of expectation values applicable in a broad range of energy densities. We estimate the desired observables by rescaling the MPS results at low bond dimensions with a factor that depends only on the fidelity of the MPS wave function. Using this technique, we simulated the dynamics of the two-dimensional Transverse-Field Ising Model (TFIM) on a 7×87\times8 grid with periodic boundary conditions, using a maximum bond dimension of χ=4096χ= 4096 on a single A100 GPU. We compared our results to similar TFIM simulations on a digital quantum processor.

Time Extrapolation with Graph Convolutional Autoencoder and Tensor Train Decomposition

Authors: Yuanhong Chen, Federico Pichi, Zhen Gao, Gianluigi Rozza

arXiv ID: 2511.23037 | Date: 2025-11-28

Abstract: Graph autoencoders have gained attention in nonlinear reduced-order modeling of parameterized partial differential equations defined on unstructured grids. Despite they provide a geometrically consistent way of treating complex domains, applying such architectures to parameterized dynamical systems for temporal prediction beyond the training data, i.e. the extrapolation regime, is still a challenging task due to the simultaneous need of temporal causality and generalizability in the parametric space. In this work, we explore the integration of graph convolutional autoencoders (GCAs) with tensor train (TT) decomposition and Operator Inference (OpInf) to develop a time-consistent reduced-order model. In particular, high-fidelity snapshots are represented as a combination of parametric, spatial, and temporal cores via TT decomposition, while OpInf is used to learn the evolution of the latter. Moreover, we enhance the generalization performance by developing a multi-fidelity two-stages approach in the framework of Deep Operator Networks (DeepONet), treating the spatial and temporal cores as the trunk networks, and the parametric core as the branch network. Numerical results, including heat-conduction, advection-diffusion and vortex-shedding phenomena, demonstrate great performance in effectively learning the dynamic in the extrapolation regime for complex geometries, also in comparison with state-of-the-art approaches e.g. MeshGraphNets.

Accurate computation of the energy variance and LL\langle\langle \mathcal{L}^\dagger \mathcal{L} \rangle\rangle using iPEPS

Authors: Emilio Cortés Estay, Naushad A. Kamar, Philippe Corboz

arXiv ID: 2511.22669 | Date: 2025-11-27

Abstract: Infinite projected entangled-pair states (iPEPS) provide a powerful tensor network ansatz for two-dimensional quantum many-body systems in the thermodynamic limit. In this paper we introduce an approach to accurately compute the energy variance of an iPEPS, enabling systematic extrapolations of the ground-state energy to the exact zero-variance limit. It is based on the contraction of a large cell of tensors using the corner transfer matrix renormalization group (CTRMG) method, to evaluate the correlator between pairs of local Hamiltonian terms. We show that the accuracy of this approach is substantially higher than that of previous methods, and we demonstrate the usefulness of variance extrapolation for the Heisenberg model, for a free fermionic model, and for the Shastry-Sutherland model. Finally, we apply the approach to compute LL\langle \langle \mathcal{L}^\dagger \mathcal{L} \rangle \rangle for an open quantum system described by the Liouvillian L\mathcal{L}, in order to assess the quality of the steady-state solution and to locate first-order phase transitions, using the dissipative quantum Ising model as an example.

Tensor complex renormalization with generalized symmetry and topological bootstrap

Authors: Dong-Yu Bao, Gong Cheng, Hong-Hao Song, Zheng-Cheng Gu

arXiv ID: 2511.22647 | Date: 2025-11-27

Abstract: Recent progress in generalized symmetry and topological holography has shown that, in conformal field theory (CFT), topological data from one dimensional higher can play a key role in determining local dynamics. Based on this insight, a fixed-point (FP) tensor complex (TC) for CFT has recently been constructed. In this work, we develop a TC renormalization (TCR) algorithm adapted to this CFT-based structure, forming a renormalization-group (RG) framework with generalized symmetry. We show that the full FP tensor can emerge from the RG flow starting with only the three-point function of the primary fields. Remarkably, even when starting solely from topological data, the RG process can still reconstruct the full FP tensor--a method we call as topological bootstrap. This approach deepens the connection between the topological and dynamical aspects of CFT and suggests pathways toward a fully algebraic description of gapless quantum states, with potential extensions to higher dimensions.

Improved parameter initialization for the (local) unitary cluster Jastrow ansatz

Authors: Wan-Hsuan Lin, Fangchun Liang, Mario Motta, Haimeng Zhang, Kenneth M. Merz, Kevin J. Sung

arXiv ID: 2511.22476 | Date: 2025-11-27

Abstract: The unitary cluster Jastrow (UCJ) ansatz and its variant known as local UCJ (LUCJ) are promising choices for variational quantum algorithms for chemistry due to their combination of physical motivation and hardware efficiency. The parameters of these ansatzes can be initialized from the output of a coupled cluster, singles and doubles (CCSD) calculation performed on a classical computer. However, truncating the number of repetitions of the ansatz, as well as discarding interactions to accommodate the connectivity constraints of near-term quantum processors, degrade the approximation to CCSD and the resulting energy accuracy. In this work, we propose two methods to improve the parameter initialization. The first method, which is applicable to both expectation value- and sample-based algorithms, uses compressed double factorization of the CCSD amplitudes to improve or recover the CCSD approximation. The second method, which is applicable to sample-based algorithms, uses approximate tensor network simulation to improve the quality of samples produced by the ansatz circuit. We validate our methods using exact state vector simulation on systems of up to 52 qubits, as well as experiments on superconducting quantum processors using up to 65 qubits. Our results indicate that our methods can significantly improve the output of both expectation value- and sample-based quantum algorithms.

Superradiant decay in non-Markovian Waveguide Quantum Electrodynamics

Authors: Rosa Lucia Capurso, Giuseppe Calajó, Simone Montangero, Saverio Pascazio, Francesco V. Pepe, Maria Maffei, Giuseppe Magnifico, Paolo Facchi

arXiv ID: 2511.22332 | Date: 2025-11-27

Abstract: An array of initially excited emitters coupled to a one-dimensional waveguide exhibits superradiant decay under the Born-Markov approximation, manifested as a coherent burst of photons in the output field. In this work, we employ tensor-network methods to investigate its non-Markovian dynamics induced by finite time delays in photon exchange among the emitters. We find that the superradiant burst breaks into a structured train of correlated photons, each intensity peak corresponding to a specific photon number. We quantify the emitter-photon and emitter-emitter entanglement generated during this process and show that the latter emerges in the long-time limit, as part of the excitation becomes trapped within the emitters' singlet subspace. We finally consider the decay of the system's most radiant state, the symmetric Dicke state, and show that time delay can lead to decay rates exceeding those predicted by the Markovian approximation.

Quantum Simulation of Ligand-like Molecules through Sample-based Quantum Diagonalization in Density Matrix Embedding Framework

Authors: Ashish Kumar Patra, Anurag K. S. V., Sai Shankar P., Ruchika Bhat, Raghavendra V., Rahul Maitra, Jaiganesh G

arXiv ID: 2511.22158 | Date: 2025-11-27

Abstract: The accurate treatment of electron correlation in extended molecular systems remains computationally challenging using classical electronic structure methods. Hybrid quantum-classical algorithms offer a potential route to overcome these limitations; however, their practical deployment on existing quantum computers requires strategies that both reduce problem size and mitigate hardware noise. In this work, we combine Density Matrix Embedding Theory (DMET) with Sample-based Quantum Diagonalization (SQD) to compute ground-state energies of a set of natural ligand-like molecules in the minimal Slater Type Orbital (STO-3G) basis set. DMET provides a systematic fragmentation of a molecule into embedded impurity subproblems, while SQD enables construction and classical diagonalization of reduced configuration spaces through quantum sampling enhanced by iterative configuration recovery. The resulting embedded Hamiltonians are solved on IBM's Eagle R3 superconducting quantum hardware (IBM Sherbrooke). The DMET-SQD energies obtained for all systems considered exhibit strong agreement with DMET-FCI benchmark values within chemical accuracy (1 kcal/mol). These results demonstrate that sample-based quantum methods, when integrated with a robust embedding framework, can reliably extend quantum computation towards simulation of chemically relevant molecular systems, showcasing potential applications in the field of drug discovery.

Holographically Emergent Gauge Theory in Symmetric Quantum Circuits

Authors: Akash Vijay, Jong Yeon Lee

arXiv ID: 2511.21685 | Date: 2025-11-26

Abstract: We develop a novel holographic framework for mixed-state phases in random quantum circuits, both unitary and non-unitary, with a global symmetry GG. Viewing the circuit as a tensor network, we decompose it into two parts: a symmetric layer, which defines an emergent gauge wavefunction in one higher dimension, and a random non-symmetric layer, which consists of random multiplicity tensors. For unitarity circuits, the bulk gauge state is deconfined, but under a generic non-unitary circuit (e.g. channels), the bulk gauge theory can undergo a decoherence-induced phase transition: for G=ZNG\,{=}\,\mathbb{Z}_N with local symmetric noise, the circuit can act as a quantum error-correcting code with a distinguished logical subspace inheriting the ZN\mathbb{Z}_N-surface code's topological protection. We then identify that the charge sharpening transition from the measurement side is complementary to a decodability transition in the bulk: noise of the bulk can be interpreted as measurement from the environment. For N4N\,{\leq}\,4, weak measurements drive a single transition from a charge-fuzzy phase with sharpening time t#eLt_{\#}\sim e^{L} to a charge-sharp phase with t#O(1)t_{\#}\sim \mathcal{O}(1), corresponding to confinement that destroys logical information. For N>4N>4, measurements generically generate an intermediate quasi-long-range ordered Coulomb phase with gapless photons and purification time t#O(L)t_{\#}\sim \mathcal{O}(L).

Holographically Emergent Gauge Theory in Symmetric Quantum Circuits

Authors: Akash Vijay, Jong Yeon Lee

arXiv ID: 2511.21685 | Date: 2025-11-26

Abstract: We develop a novel holographic framework for mixed-state phases in random quantum circuits, both unitary and non-unitary, with a global symmetry GG. Viewing the circuit as a tensor network, we decompose it into two parts: a symmetric layer, which defines an emergent gauge wavefunction in one higher dimension, and a random non-symmetric layer, which consists of random multiplicity tensors. For unitarity circuits, the bulk gauge state is deconfined, but under a generic non-unitary circuit (e.g. channels), the bulk gauge theory can undergo a decoherence-induced phase transition: for G=ZNG\,{=}\,\mathbb{Z}_N with local symmetric noise, the circuit can act as a quantum error-correcting code with a distinguished logical subspace inheriting the ZN\mathbb{Z}_N-surface code's topological protection. We then identify that the charge sharpening transition from the measurement side is complementary to a decodability transition in the bulk: noise of the bulk can be interpreted as measurement from the environment. For N4N\,{\leq}\,4, weak measurements drive a single transition from a charge-fuzzy phase with sharpening time t#eLt_{\#}\sim e^{L} to a charge-sharp phase with t#O(1)t_{\#}\sim \mathcal{O}(1), corresponding to confinement that destroys logical information. For N>4N>4, measurements generically generate an intermediate quasi-long-range ordered Coulomb phase with gapless photons and purification time t#O(L)t_{\#}\sim \mathcal{O}(L).

Rapid ground state energy estimation with a Sparse Pauli Dynamics-enabled Variational Double Bracket Flow

Authors: Chinmay Shrikhande, Arnab Bachhar, Aaron Rodriguez Jimenez, Nicholas J. Mayhall

arXiv ID: 2511.21651 | Date: 2025-11-26

Abstract: Ground state energy estimation for strongly correlated quantum systems remains a central challenge in computational physics and chemistry. While tensor network methods like DMRG provide efficient solutions for one-dimensional systems, higher-dimensional problems remain difficult. Here we present a variational double bracket flow (vDBF) algorithm that leverages Sparse Pauli Dynamics, a technique originally developed for classical simulation of quantum circuits, to efficiently approximate ground state energies. By combining greedy operator selection with coefficient truncation and energy-variance extrapolation, the method achieves less than 1% error relative to DMRG benchmarks for both Heisenberg and Hubbard models in one and two dimensions. For a 10x10 Heisenberg lattice (100 qubits), vDBF obtains accurate results in approximately 10 minutes on a single CPU thread, compared to over 50 hours on 64 threads for DMRG. For an 8x8 Hubbard model (128 qubits), the speedup is even more pronounced. These results demonstrate that classical simulation techniques developed in the context of quantum advantage benchmarking can provide practical tools for many-body physics.

Non-semisimple CFT/TFT correspondence I: General setup

Authors: Aaron Hofer, Ingo Runkel

arXiv ID: 2511.21231 | Date: 2025-11-26

Abstract: We extend the TFT construction of CFT correlators of [arXiv:hep-th/0204148] to so-called finite logarithmic CFTs for which the algebraic input data is no longer semisimple but still finite. More specifically, starting from the data of a chiral CFT given in the form of a not necessarily semisimple modular tensor category C we use a three dimensional topological field theory with surface defects based on the surgery TFT of [arXiv:1912.02063] to construct a full CFT as a braided monoidal oplax natural transformation. We make our construction explicit in the example of the transparent surface defect, resulting in the so-called Cardy case. In particular, we consider topological line defects and their action on bulk fields in these logarithmic CFTs, providing a source of examples for non-invertible and non-semisimple topological symmetries.

Multi-Field Relativistic Continuous Matrix Product States

Authors: Karan Tiwana, Antoine Tilloy

arXiv ID: 2511.20762 | Date: 2025-11-25

Abstract: Relativistic continuous matrix product states (RCMPS) are a powerful variational ansatz for quantum field theories of a single field. However, they inherit a property of their non-relativistic counterpart that makes them divergent for models with multiple fields, unless a regularity condition is satisfied. This has so far restricted the use of RCMPS to toy models with a single self-interacting field. We address this long standing problem by introducing a Riemannian optimization framework, that allows to minimize the energy density over the regular submanifold of multi-field RCMPS, and thus to retain purely variational results. We demonstrate its power on a model of two interacting scalar fields in 1+11+1 dimensions. The method captures distinct symmetry-breaking phases, and the signature of a Berezinskii-Kosterlitz-Thouless (BKT) transition along an O(2)O(2)-symmetric parameter line. This makes RCMPS usable for a far larger class of problems than before.

Multi-Field Relativistic Continuous Matrix Product States

Authors: Karan Tiwana, Antoine Tilloy

arXiv ID: 2511.20762 | Date: 2025-11-25

Abstract: Relativistic continuous matrix product states (RCMPS) are a powerful variational ansatz for quantum field theories of a single field. However, they inherit a property of their non-relativistic counterpart that makes them divergent for models with multiple fields, unless a regularity condition is satisfied. This has so far restricted the use of RCMPS to toy models with a single self-interacting field. We address this long standing problem by introducing a Riemannian optimization framework, that allows to minimize the energy density over the regular submanifold of multi-field RCMPS, and thus to retain purely variational results. We demonstrate its power on a model of two interacting scalar fields in 1+11+1 dimensions. The method captures distinct symmetry-breaking phases, and the signature of a Berezinskii-Kosterlitz-Thouless (BKT) transition along an O(2)O(2)-symmetric parameter line. This makes RCMPS usable for a far larger class of problems than before.

Extracting conserved operators from a projected entangled pair state

Authors: Wen-Tao Xu, Miguel Frías Pérez, Mingru Yang

arXiv ID: 2511.20619 | Date: 2025-11-25

Abstract: Given a tensor network state, how can we determine conserved operators (including Hamiltonians) for which the state is an eigenstate? We answer this question by presenting a method to extract geometrically kk-local conserved operators that have the given infinite projected entangled pair state (iPEPS) in 2D as an (approximate) eigenstate. The key ingredient is the evaluation of the static structure factors of multi-site operators through differentiating the generating function. Despite the approximation errors, we show that our method is still able to extract from exact or variational iPEPS to good precision both frustration-free and non-frustration-free parent Hamiltonians that are beyond the standard construction and obtain better locality. In particular, we find a 4-site-plaquette local Hamiltonian that approximately has the short-range RVB state as the ground state. Moreover, we find a Hamiltonian that has the deformed toric code state at any string tension as excited eigenstates at the same energy, which might be potential candidates for quantum many-body scars.

A Fully Probabilistic Tensor Network for Regularized Volterra System Identification

Authors: Afra Kilic, Kim Batselier

arXiv ID: 2511.20457 | Date: 2025-11-25

Abstract: Modeling nonlinear systems with Volterra series is challenging because the number of kernel coefficients grows exponentially with the model order. This work introduces Bayesian Tensor Network Volterra kernel machines (BTN-V), extending the Bayesian Tensor Network framework to Volterra system identification. BTN-V represents Volterra kernels using canonical polyadic decomposition, reducing model complexity from O(I^D) to O(DIR). By treating all tensor components and hyperparameters as random variables, BTN-V provides predictive uncertainty estimation at no additional computational cost. Sparsity-inducing hierarchical priors enable automatic rank determination and the learning of fading-memory behavior directly from data, improving interpretability and preventing overfitting. Empirical results demonstrate competitive accuracy, enhanced uncertainty quantification, and reduced computational cost.

Resource assessment of classical and quantum hardware for post-quench dynamics

Authors: Joseph Vovrosh, Tiago Mendes-Santos, Hadriel Mamann, Kemal Bidzhiev, Fergus Hayes, Bruno Ximenez, Lucas Béguin, Constantin Dalyac, Alexandre Dauphin

arXiv ID: 2511.20388 | Date: 2025-11-25

Abstract: We estimate the run-time and energy consumption of simulating non-equilibrium dynamics on neutral atom quantum computers in analog mode, directly comparing their performance to state-of-the-art classical methods, namely Matrix Product States and Neural Quantum States. By collecting both experimental data from a quantum processing unit (QPU) in analog mode and numerical benchmarks, we enable accurate predictions of run-time and energy consumption for large-scale simulations on both QPUs and classical systems through fitting of theoretical scaling laws. Our analysis shows that neutral atom devices are already operating in a competitive regime, achieving comparable or superior performance to classical approaches while consuming significantly less energy. These results demonstrate the potential of analog neutral atom quantum computing for energy-efficient simulation and highlight a viable path toward sustainable computational strategies.

Disentangling Kitaev Quantum Spin Liquid

Authors: Xiang Li, Xiangjian Qian, Mingpu Qin

arXiv ID: 2511.20261 | Date: 2025-11-25

Abstract: In this work, we investigate the Kitaev honeycomb model employing the recently developed Clifford Circuits Augmented Matrix Product States (CAMPS) method. While the model in the gapped phase is known to reduce to the toric code model - whose ground state is entirely constructible from Clifford circuits - we demonstrate that the very different gapless quantum spin liquid (QSL) phase can also be significantly disentangled with Clifford circuits. Specifically, CAMPS simulations reveal that approximately two-thirds of the entanglement entropy in the isotropic point arises from Clifford-circuit contributions, enabling dramatically more efficient computations compared to conventional matrix product state (MPS) methods. Crucially, this finding implies that the Kitaev QSL state retains significant Clifford-simulatable structure, even in the gapless phase with non-abelian anyon excitations when time reversal symmetry is broken. This property not only enhances classical simulation efficiency significantly but also suggests substantial resource reduction for preparing such states on quantum devices. As an application, we leverage CAMPS to study the Kitaev-Heisenberg model and determine the most accurate phase boundary between the anti-ferromagnetic phase and the Kitaev QSL phase in the model. Our results highlight how Clifford circuits can effectively disentangle the intricate entanglement of Kitaev QSLs, opening avenues for efficiently simulating related and similar strongly correlated models.

No-go theorems for sequential preparation of two-dimensional chiral states via channel-state correspondence

Authors: Ruihua Fan, Yantao Wu, Yimu Bao, Zhehao Dai

arXiv ID: 2511.19612 | Date: 2025-11-24

Abstract: We investigate whether sequential unitary circuits can prepare two-dimensional chiral states, using a correspondence between sequentially prepared states, isometric tensor network states, and one-dimensional quantum channel circuits. We establish two no-go theorems, one for Gaussian fermion systems and one for generic interacting systems. In Gaussian fermion systems, the correspondence relates the defining features of chiral wave functions in their entanglement spectrum to the algebraic decaying correlations in the steady state of channel dynamics. We establish the no-go theorem by proving that local channel dynamics with translational invariance cannot support such correlations. As a direct implication, two-dimensional Gaussian fermion isometric tensor network states cannot support algebraically decaying correlations in all directions or represent a chiral state. In generic interacting systems, we establish a no-go theorem by showing that the state prepared by sequential circuits cannot host the tripartite entanglement of a chiral state due to the constraints from causality.

Holographic duality between bulk topological order and boundary mixed-state order

Authors: Tsung-Cheng Lu, Yu-Jie Liu, Sarang Gopalakrishnan, Yizhi You

arXiv ID: 2511.19597 | Date: 2025-11-24

Abstract: We introduce a holographic framework for analyzing the steady states of repeated quantum channels with strong symmetries. Using channel-state duality, we show that the steady state of a dd-dimensional quantum channel is holographically mapped to the boundary reduced density matrix of a (d+1)(d+1)-dimensional wavefunction generated by a sequential unitary circuit. From this perspective, strong-to-weak spontaneous symmetry breaking (SWSSB) in the steady state arises from the anyon condensation on the boundary of a topological order in one higher dimension. The conditional mutual information (CMI) associated with SWSSB is then inherited from the bulk topological entanglement entropy. We make this duality explicit using isometric tensor network states (isoTNS) by identifying the channel's time evolution with the transfer matrix of a higher-dimensional isoTNS. Built on isoTNS, we further construct continuously tunable quantum channels that exhibit distinct mixed-state phases and transitions in the steady states.

Simulating dynamics of the two-dimensional transverse-field Ising model: a comparative study of large-scale classical numerics

Authors: Joseph Vovrosh, Sergi Julià-Farré, Wladislaw Krinitsin, Michael Kaicher, Fergus Hayes, Emmanuel Gottlob, Augustine Kshetrimayum, Kemal Bidzhiev, Simon B. Jäger, Markus Schmitt, Joseph Tindall, Constantin Dalyac, Tiago Mendes-Santos, Alexandre Dauphin

arXiv ID: 2511.19340 | Date: 2025-11-24

Abstract: The quantum dynamics of many-qubit systems is an outstanding problem that has recently driven significant advances in both numerical methods and programmable quantum processing units. In this work, we employ a comprehensive toolbox of state-of-the-art numerical approaches to classically simulate the dynamics of the two-dimensional transverse field Ising model. Our methods include three different tensor network techniques -- matrix product states, tree-tensor networks, and two-dimensional tensor-networks under the belief propagation approximation -- as well as time-dependent variational Monte Carlo with Neural Quantum States. We focus on two paradigmatic dynamical protocols: (i) quantum annealing through a critical point and (ii) post-quench dynamics. Our extensive results show the quantitative predictions of various state-of-the-art numerical methods providing a benchmark for future numerical investigations and experimental studies with the aim to push the limitations on classical and QPUs. In particular, our work connects classical simulability to different regimes associated with quantum dynamics in Rydberg arrays - namely, quasi-adiabatic dynamics, the Kibble-Zurek mechanism, and quantum quenches.

Competition between charge-density-wave and superconducting orders on eight-leg square Hubbard cylinders

Authors: Hong-Chen Jiang, Thomas P. Devereaux, Steven A. Kivelson

arXiv ID: 2511.18644 | Date: 2025-11-23

Abstract: The issue of whether dd-wave superconductivity (SC) occurs in the square-lattice Hubbard model with UU of order of the bandwidth has been one of the most debated issues to emerge from the study of high temperature SC. Here, we report variational results on eight-leg cylinders with next-nearest-neighbor hopping in the range 0.5tt0.25t-0.5 t \leq t'\leq 0.25 t with U=8tU = 8t and 12t12t and doped hole concentrations δ=1/12δ=1/12 and 1/81/8. For t0t'\leq 0, the ground-state appears to be a charge-density wave (CDW) of one sort or another with SC correlations that are extremely short-ranged. In contrast, in some cases, the local magnetic order has a correlation length greater than half the cylinder width - suggestive that magnetic order might also arise in the 2D limit. For t>0t'>0, our results depend more strongly on boundary conditions (periodic vs antiperiodic), making it still harder to correctly guess whether SC or CDW correlations dominate in the 2D limit. These results were obtained employing matrix-product states with bond dimensions large enough that energy differences as small as 103t10^{-3}t per site can be resolved.

Comprehensive Design Space Exploration for Tensorized Neural Network Hardware Accelerators

Authors: Jinsong Zhang, Minghe Li, Jiayi Tian, Jinming Lu, Zheng Zhang

arXiv ID: 2511.17971 | Date: 2025-11-22

Abstract: High-order tensor decomposition has been widely adopted to obtain compact deep neural networks for edge deployment. However, existing studies focus primarily on its algorithmic advantages such as accuracy and compression ratio-while overlooking the hardware deployment efficiency. Such hardware-unaware designs often obscure the potential latency and energy benefits of tensorized models. Although several works attempt to reduce computational cost by optimizing the contraction sequence based on the number of multiply-accumulate operations, they typically neglect the underlying hardware characteristics, resulting in suboptimal real-world performance. We observe that the contraction path, hardware architecture, and dataflow mapping are tightly coupled and must be optimized jointly within a unified design space to maximize deployment efficiency on real devices. To this end, we propose a co-exploration framework that unifies these dimensions within a unified design space for efficient training and inference of tensorized neural networks on edge platforms. The framework formulates a latency oriented search objective and solves it via a global latency-driven exploration across the unified design space to achieve end-to-end model efficiency. The optimized configurations are implemented on a configurable FPGA kernel, achieving up to 4x and 3.85x lower inference and training latency compared with the dense baseline.

Kicked-Ising Quantum Battery

Authors: Sebastián V. Romero, Xi Chen, Yue Ban

arXiv ID: 2511.17835 | Date: 2025-11-21

Abstract: Quantum batteries (QBs) have emerged as promising candidates capable of outperforming classical counterparts by utilizing entangled operators. Spin chains, in particular, exhibit unique {charging} properties across diverse settings. Here, we introduce the kicked-Ising model as a QB and analytically characterize its charging dynamics within the self-dual operator regime, valid for arbitrary system sizes and Floquet cycles. Using Clifford quantum cellular automata and momentum-space Floquet analysis with the Cayley-Hamilton theorem, we obtain exact expressions for energy injection, uncovering the influence of boundary conditions and spin-chain parity on charging performance. The kicked-Ising QB achieves maximal charging while exhibiting remarkable robustness against disorder. We further propose an intensified protocol within a fixed time window that enables faster and more efficient energy injection, while non-uniform kick schedules enhance experimental flexibility. Spin correlators analysis further shows that low-frequency driving boosts energy injection, highlighting a clear connection between charging, scrambling, and kick-induced delocalization. Our theoretical framework are supported by tensor-network simulations and finally verified on IBM quantum hardware. Accounting for platform-specific constraints, we demonstrate that the kicked-Ising QB offers a scalable, disorder-resilient protocol and testbed to assess quantum platforms.

Tensor network simulations of quasi-GPDs in the massive Schwinger model

Authors: Sebastian Grieninger, Jake Montgomery, Felix Ringer, Ismail Zahed

arXiv ID: 2511.17752 | Date: 2025-11-21

Abstract: Generalized Parton Distribution functions (GPDs) are off-diagonal light-cone matrix elements that encode the internal structure of hadrons in terms of quark and gluon degrees of freedom. In this work, we present the first nonperturbative study of quasi-GPDs in the massive Schwinger model, quantum electrodynamics in 1+1 dimensions (QED2), within the Hamiltonian formulation of lattice field theory. Quasi-distributions are spatial correlation functions of boosted states, which approach the relevant light-cone distributions in the luminal limit. Using tensor networks, we prepare the first excited state in the strongly coupled regime and boost it to close to the light-cone on lattices of up to 400 lattice sites. We compute both quasi-parton distribution functions and, for the first time, quasi-GPDs, and study their convergence for increasingly boosted states. In addition, we perform analytic calculations of GPDs in the two-particle Fock-space approximation and in the Reggeized limit, providing qualitative benchmarks for the tensor network results. Our analysis establishes computational benchmarks for accessing partonic observables in low-dimensional gauge theories, offering a starting point for future extensions to higher dimensions, non-Abelian theories, and quantum simulations.

Teaching quantum computing to computer science students: Review of a hands-on quantum circuit simulation practical

Authors: Florian Krötz, Xiao-Ting Michelle To, Korbinian Staudacher, Dieter Kranzlmüller

arXiv ID: 2511.17218 | Date: 2025-11-21

Abstract: We present a practical course targeting graduate students with prior knowledge of the basics of quantum computing. The practical aims to deepen students' understanding of fundamental concepts in quantum computing by implementing quantum circuit simulators. Through hands-on experience, students learn about different methods to simulate quantum computing, including state vectors, density matrices, the stabilizer formalism, and matrix product states. By implementing the simulation methods themselves, students develop a more in-depth understanding of fundamental concepts in quantum computing, including superposition, entanglement, and the effects of noise on quantum systems. This hands-on experience prepares students to do research in the field of quantum computing and equips them with the knowledge and skills necessary to tackle complex research projects in the field. In this work, we describe our teaching approach and the structure of our practical, and we discuss evaluations and lessons learned.

Probing Boundary Spins in the Su-Schrieffer-Heeger-Hubbard model

Authors: Armando A. Aligia, Alejandro M. Lobos, Lucila Peralta Gavensky, Claudio J. Gazza

arXiv ID: 2511.17173 | Date: 2025-11-21

Abstract: Studying boundary excitations provides a powerful approach to probe correlations in topological phases. We propose that localized spins near the ends of a Su-Schrieffer-Heeger-Hubbard chain embedded in an insulating environment can be detected experimentally using scanning tunneling microscopy (STM) combined with electron spin resonance (ESR). When the STM tip is in the contact regime, the tip-end-spin coupling realizes an effective Anderson impurity problem, giving rise to a Kondo peak at low bias. Spatially resolving the Kondo resonance width as the STM tip approaches the chain ends provides an indirect yet clear signature of these localized spins. To support this proposal, we use density-matrix renormalization group (DMRG) to calculate the spin gap and spin projection of end states for chains of various lengths and interaction strengths UU at half-filling. In the non-interacting limit (U=0U=0), we derive simple analytical expressions that reproduce the numerical results for sufficiently long chains. We also discuss how the correlated phase of the isolated chain is characterized by boundary zeros in its single-particle Green's function, and briefly comment on their localization properties in relation to the boundary spins.

Pair scattering from time-modulated impurity in the Bose-Hubbard model

Authors: Neda Ahmadi, Ameneh Sheikhan, Corinna Kollath

arXiv ID: 2511.17032 | Date: 2025-11-21

Abstract: We investigate scattering phenomena in a one-dimensional attractive Bose-Hubbard model with a time-periodically modulated impurity. We analyze both single-particle and pair (doublon) transmission, exploring a range of interaction strengths and drive amplitudes. Our exact numerical results reveal excellent quantitative agreement with analytical predictions in the high-frequency limit. At intermediate and weak attractive interactions, we observe significant pair dissociation and the emergence of dynamically localized single-particle modes. These features are reminiscent of Floquet Bound States in the Continuum (BICs). These findings provide new avenues for engineering controllable quantum transport and localized states in ultracold atom experiments.

Excited states from local effective Hamiltonians of matrix product states and their entanglement spectrum transition

Authors: Denise Cocchiarella, Mingru Yang, Yueshui Zhang, Mari Carmen Bañuls, Hong-Hao Tu, Yuhan Liu

arXiv ID: 2511.16746 | Date: 2025-11-20

Abstract: Solving excited states is a challenging task for interacting systems. For one-dimensional critical systems, however, excited states can be directly accessed from the eigenvectors of the local effective Hamiltonian that is constructed from the ground state obtained by variational matrix product state (MPS) optimization. Despite its numerical success, the theoretical mechanism underlying this method has remained largely unexplored. In this work, we provide a conformal field theory (CFT) perspective that helps elucidate this connection. The key insight is that this construction effectively uses a truncated basis of ground-state Schmidt vectors to represent excited states, where the contribution of each Schmidt vector can be expressed as a CFT correlation function and shown to decay with increasing Schmidt index. The CFT analysis further predicts an entanglement-spectrum transition of excited states as the ratio of the subsystem size to the total system size is varied. Our numerical results support this picture and demonstrate a reorganization of the entanglement spectrum into distinct conformal towers as this ratio changes.

Conserved quantities enable the quantum Mpemba effect in weakly open systems

Authors: Iris Ulčakar, Rustem Sharipov, Gianluca Lagnese, Zala Lenarčič

arXiv ID: 2511.16739 | Date: 2025-11-20

Abstract: Observation of the quantum Mpemba effect has spurred much interest in its enabling conditions and its relation to the classical counterpart. Here, we consider weakly open many-body quantum systems initialized in different thermal states and examine when the initially farther state relaxes to the (non-equilibrium) steady state faster. We claim that the number of conserved quantities in the unitary part plays a crucial role: the Mpemba effect is possible only when the Hamiltonian commutes with other extensive operators or is integrable. The reason lies in the dynamical evolution happening in spaces of different dimensions. When energy is the only approximately conserved quantity, dissipation pushes the dynamics within a single-parameter manifold of different thermal states. In contrast, for Hamiltonians with several conserved quantities, the dynamics drift in the multi-dimensional space of generalized Gibbs ensembles, whose distance to the steady state is less trivial. We provide numerical results for large system sizes using tensor networks and free-fermion techniques, thereby supporting our claim.

Stabilizing Fractional Chern States in Twisted MoTe2: Multi-band Correlations via Non-perturbative Renormalization Group

Authors: Run Hou, Andriy H. Nevidomskyy

arXiv ID: 2511.16641 | Date: 2025-11-20

Abstract: The observation of fraction quantum Hall states in twisted MoTe2 has sparked a lof of interest in this phenomenon. Most theoretical works to date rely on the brute-force exact diagonalization which is limited to the one partially occupied band. In this work, we present strong evidence that the effect of higher lying bands cannot be ignored due to strong interband interactions. To tackle these effects, we introduce a non-perturbative driven similarity renormalization group (DSRG) method, originally developed for problems in quantum chemistry. We apply this methodology to twisted MoTe2 at fractional hole fillings of ν = 1/3 and 2/3 across a spectrum of twist angles. Our results show that at ν = 1/3, the many-body excitation energy gaps are substantially reduced compared to the one-band treatment. For ν = 2/3, we find that the dynamic correlations stemming from interband interactions stabilize fractional Chern insulating phases at larger twist angles, consistent with the experimental findings. By examining the correlated orbitals and their single-particle topological features, we demonstrate that this stabilization at higher twist angles arises predominantly from the dynamic correlations, rather than conditions on the single-particle quantum geometric tensor.

OpenQudit: Extensible and Accelerated Numerical Quantum Compilation via a JIT-Compiled DSL

Authors: Ed Younis

arXiv ID: 2511.16585 | Date: 2025-11-20

Abstract: High-performance numerical quantum compilers rely on classical optimization, but are limited by slow numerical evaluations and a design that makes extending them with new instructions a difficult, error-prone task for domain experts. This paper introduces OpenQudit, a compilation framework that solves these problems by allowing users to define quantum operations symbolically in the Qudit Gate Language (QGL), a mathematically natural DSL. OpenQudit's ahead-of-time compiler uses a tensor network representation and an e-graph-based pass for symbolic simplification before a runtime tensor network virtual machine (TNVM) JIT-compiles the expressions into high-performance native code. The evaluation shows that this symbolic approach is highly effective, accelerating the core instantiation task by up to 20×\mathtt{\sim}20\times on common quantum circuit synthesis problems compared to state-of-the-art tools.

Order-by-disorder from Schwinger bosons in a frustrated honeycomb ferromagnet

Authors: Arnaud Ralko, Jaime Merino

arXiv ID: 2511.16429 | Date: 2025-11-20

Abstract: The cobalt-based honeycomb magnet BaCo2_2(AsO4_4)2_2 (BCAO) has recently emerged as a promising platform for studying frustrated magnetism beyond conventional paradigms. Neutron-scattering experiments and first-principles calculations have revealed an unexpected double-zigzag (dZZ) magnetically ordered ground state, whose microscopic origin remains under active debate. Here, we investigate the emergence of such dZZ phase in a ferro-antiferromagnetic J1J_1-J3J_3 Heisenberg model on the honeycomb lattice, using a generalized Schwinger boson mean-field theory (gg-SBMFT) that treats ferromagnetic and antiferromagnetic interactions on equal footing. Based on gg-SBMFT and exact-diagonalization (ED) techniques, we find that the dZZ is selected by an order-by-disorder mechanism in a narrow J3/J1J_3/|J_1| range, in agreement with recent density-matrix renormalization-group calculations. The magnetic excitation spectra within the dZZ phase displays a distinctive smearing out in momentum space due to quantum fluctuations which may be probed through inelastic neutron-scattering experiments.

iFCTN: Folding-Free Fully-Connected Tensor Network Decomposition for Tensor Completion

Authors: Ziyi Gan, Chunfeng Cui

arXiv ID: 2511.16358 | Date: 2025-11-20

Abstract: The fully-connected tensor network (FCTN) decomposition has recently exhibited strong modeling capabilities by connecting every pair of tensor factors, thereby capturing rich cross-mode correlations and maintaining invariance under mode transpositions. However, this advantage comes with an inherent limitation: updating the factors typically requires reconstructing auxiliary sub-networks, which entails extensive and cumbersome (un)folding. In this study, we propose intra-block FCTN (iFCTN) decomposition, a novel (un)folding-free variant of FCTN decomposition that streamlines computation. We parameterize each FCTN factor through Khatri-Rao products, which significantly reduces the complexity of reconstructing intermediate sub-networks and yields subproblems with well-structured coefficient matrices. Furthermore, we deploy the proposed iFCTN decomposition on the representative task of tensor completion and design an efficient proximal alternating minimization algorithm while retaining convergence guarantees. Extensive experiments demonstrate that iFCTN outperforms or matches state-of-the-art methods with comparable computational cost.

Real-time Scattering in φ^4 Theory using Matrix Product States

Authors: Bahaa Al Sayegh, Wissam Chemissany

arXiv ID: 2511.15697 | Date: 2025-11-19

Abstract: We investigate the critical behavior and real-time scattering dynamics of the interacting φ4φ^4 quantum field theory in (1+1)(1+1) dimensions using uniform matrix product states and the time-dependent variational principle. A finite-entanglement scaling analysis at λ=0.8λ= 0.8 bounds the critical mass-squared to μc2[0.3190,0.3185]μ_c^2 \in [-0.3190,-0.3185] and provides a quantitative map of the symmetric, near-critical, weakly broken, and deeply broken regimes. Using these ground states as asymptotic vacua, we simulate two-particle collisions in a sandwich geometry and extract the elastic scattering probability P1111(E)P_{11\to 11}(E) and Wigner time delay Δt(E)Δt(E) following the prescription of Jha et al. [Phys. Rev. Research 7, 023266 (2025)]. We find strongly inelastic scattering in the symmetric phase (P11110.63P_{11\to 11} \simeq 0.63, Δt180Δt \simeq -180 for μ2=0.2μ^2 = 0.2), almost perfectly elastic collisions in the spontaneously broken phase (P11110.998P_{11\to 11} \simeq 0.998, Δt270Δt \simeq -270 for μ2=0.2μ^2=-0.2 and P11111P_{11\to 11} \simeq 1, Δt177.781Δt \simeq -177.781 for μ2=0.5μ^2=-0.5), and a breakdown of the sandwich evolution precisely at the critical coupling, which provides a dynamical signature of the quantum critical point. These results demonstrate that TDVP-based uniform matrix product states can probe nonperturbative scattering and critical dynamics in lattice φ4φ^4 theory with controlled entanglement truncation.

Efficient quantum state preparation of multivariate functions using tensor networks

Authors: Marco Ballarin, Juan José García-Ripoll, David Hayes, Michael Lubasch

arXiv ID: 2511.15674 | Date: 2025-11-19

Abstract: For the preparation of high-dimensional functions on quantum computers, we introduce tensor network algorithms that are efficient with regard to dimensionality, optimize circuits composed of hardware-native gates and take gate errors into account during the optimization. To avoid the notorious barren plateau problem of vanishing gradients in the circuit optimization, we smoothly transform the circuit from an easy-to-prepare initial function into the desired target function. We show that paradigmatic multivariate functions can be accurately prepared such as, by numerical simulations, a 17-dimensional Gaussian encoded in the state of 102 qubits and, through experiments, a 9-dimensional Gaussian realized using 54 qubits on Quantinuum's H2 quantum processor.

Magnetic electron-hole asymmetry in cuprates: a computational revisit

Authors: Jiong Mei, Shao-Hang Shi, Ping Xu, Ziyan Chen, Hui-Ke Jin, Mingpu Qin, Zi-Xiang Li, Kun Jiang

arXiv ID: 2511.15608 | Date: 2025-11-19

Abstract: In this work, we revisit the electron-hole asymmetry of antiferromagnetism in cuprates by studying the three-band Emery model. Using parameters relevant to La2_2CuO4_4, we benchmark the anti-ferromagnetic response for a large range of dopings with variational Monte Carlo, determinant quantum Monte Carlo, constrained-path auxiliary-field quantum Monte Carlo, density-matrix embedding theory, and the Gutzwiller approximation. Across methods and accessible sizes/temperatures, we find no significant electron-hole asymmetry if we consider only Neel anti-ferronagnetic response and ignore other possible orders such as stripe state. This result is robust to a moderate oxygen-site repulsion UpU_p and to parameter sets of Nd2_2CuO4_4. Incorporating dopant-induced local potentials reveals an extrinsic route to asymmetry: Cu-site defects enhance AFM on the electron-doped side, whereas O-site defects suppress it on the hole-doped side. These results indicate that dopant-driven effects make a non-negligible contribution to apparent electron-hole asymmetry in the general phase diagram of cuprates and should be included when analyzing competing orders in cuprates.

Spinon excitations and spin correlations in the one-dimensional quantum magnet ββ-VOSO4_4 probed by Raman spectroscopy

Authors: Dirk Wulferding, Diana Lucia Quintero-Castro, Pontus Laurell, Gonzalo Alvarez, Elbio Dagotto, Kwang-Yong Choi

arXiv ID: 2511.15452 | Date: 2025-11-19

Abstract: Fractionalized excitations such as spinons and anyons have emerged as a central theme in condensed matter physics with broad implications for superconductivity, quantum statistics, and quantum computation. The nearly ideal one-dimensional S=1/2S=1/2 system ββ-VOSO4_4 without long-range order down to 85 mK provides a promising platform to experimentally explore such fractionalized excitations. Here, we employ Raman spectroscopy to probe magnetic excitations and the evolution of spin correlations in ββ-VOSO4_4. Spinon signatures are found along the chain direction, evidenced by a broad, gapless scattering continuum at low temperatures. The temperature dependence of the spinon spectral weight aligns considerably with numerical density matrix renormalization group calculations. By comparing the experimental spinon spectral weight with calculated results and evaluating the associated quantum Fisher information (QFI) therefrom, we observe a steep increase in QFI upon cooling, indicating rapidly growing correlation lengths. Our study showcases QFI as a probe of spin correlations in quantum magnets.

Tensor-network approach to quantum optical state evolution beyond the Fock basis

Authors: Nikolay Kapridov, Egor Tiunov, Dmitry Chermoshentsev

arXiv ID: 2511.15295 | Date: 2025-11-19

Abstract: Understanding the quantum evolution of light in nonlinear media is central to the development of next-generation quantum technologies. Yet modeling these processes remains computationally demanding, as the required resources grow rapidly with photon number and phase-space resolution. Here we introduce a tensor-network approach that efficiently captures the dynamics of nonlinear optical systems in a continuous-variable representation. Using the matrix product state (MPS) formalism, both quantum states and operators are encoded in a highly compressed form, enabling direct numerical integration of the Schrödinger equation. We demonstrate the method by simulating degenerate spontaneous parametric down-conversion (SPDC) and show that it accurately reproduces established theoretical benchmarks - energy conservation, pump depletion, and quadrature squeezing - even in regimes where conventional Fock-basis simulations become infeasible. For high-intensity pump fields (α=100α= 100), the MPS representation achieves compression ratios above 31033\cdot 10^3 while preserving physical fidelity. This framework opens a scalable route to modeling multimode quantum light and nonlinear optical phenomena beyond the reach of traditional methods.

Pure gapped ground states of spin chains are short-range entangled

Authors: Wojciech De Roeck, Martin Fraas, Bruno de O. Carvalho

arXiv ID: 2511.14699 | Date: 2025-11-18

Abstract: We consider spin chains with a finite range Hamiltonian. For reasons of simplicity, the chain is taken to be infinitely long. A ground state is said to be a unique gapped ground state if its GNS Hamiltonian has a unique ground state, separated by a gap from the rest of the spectrum. By combining some powerful techniques developed in the last years, we prove that each unique gapped ground state is short-range entangled: It can be mapped into a product state by a finite time evolution map generated by a Hamiltonian with exponentially quasi-local interaction terms. This claim makes precise the common belief that one-dimensional gapped systems are topologically trivial in the bulk.

Optimizing two-dimensional isometric tensor networks with quantum computers

Authors: Sebastian Leontica, Alberto Baiardi, Julian Schuhmacher, Francesco Tacchino, Ivano Tavernelli

arXiv ID: 2511.13827 | Date: 2025-11-17

Abstract: We propose a hybrid quantum-classical algorithm for approximating the ground state of two-dimensional quantum systems using an isometric tensor network ansatz, which maps naturally to quantum circuits. Inspired by the density matrix renormalization group, we optimize tensors sequentially by diagonalizing a series of effective Hamiltonians. These are constructed using a tomography-inspired method on a qubit subset whose size depends only on the bond dimension. Our approach leverages quantum computers to enable accurate solutions without relying on approximate contractions, circumventing the exponential complexity faced by classical techniques. We demonstrate our method on the two-dimensional (2D) transverse-field Ising model, achieving ground-state optimization on up to 25 qubits with modest quantum overhead -- significantly less than standard solutions based on variational quantum eigensolvers. Overall, our results offer a path towards scalable variational quantum algorithms in both noisy and fault-tolerant regimes.

Skeleton of isometric Tensor Network States for Abelian String-Net Models

Authors: Julian Boesl, Yu-Jie Liu, Frank Pollmann, Michael Knap

arXiv ID: 2511.13821 | Date: 2025-11-17

Abstract: We construct parametrized isometric tensor network states -- referred to as skeletons -- that allow us to explore phases of abelian topological order and can be efficiently implemented on quantum processors. We obtain stable finite correlation length deformations of string-net fixed points, which are constructed both by conserving virtual symmetries of the tensor and by imposing local isometry constraints. They connect distinct topological phases via a shared critical point, thereby providing analytically tractable examples of phase transitions beyond anyon condensation. By mapping such classes of 2D tensor networks to 1D stochastic automata with local update rules, we show that expectation values of generalized Pauli strings of arbitrary weight can be efficiently computed using classical methods. Therefore these skeletons not only serve as an organizing principle for abelian topological order but also provide a non-trivial testbed for quantum processors.

Quantum complexity across thermal phase transition in the transverse field Ising chain with long-range couplings

Authors: Meghadeepa Adhikary, Nishan Ranabhat, Mario Collura

arXiv ID: 2511.13667 | Date: 2025-11-17

Abstract: We investigate the behavior of the Schmidt gap, the von Neumann entanglement entropy, and the non-stabiliserness in proximity to the classical phase transition of the one-dimensional long-range transverse-field Ising model (LRTFIM). Leveraging the time-dependent variational principle (TDVP) within a tensor-network formulation, we simulate thermal states through their purified tensor-network representations. Our results show that these observables, typically regarded as hallmarks of quantum criticality, exhibit pronounced and coherent signatures even at a classical thermal transition, highlighting the emergence of quantum complexity as the system nears thermal criticality.

A Quantum Tensor Network-Based Viewpoint for Modeling and Analysis of Time Series Data

Authors: Pragatheeswaran Vipulananthan, Kamal Premaratne, Dilip Sarkar, Manohar N. Murthi

arXiv ID: 2511.13514 | Date: 2025-11-17

Abstract: Accurate uncertainty quantification is a critical challenge in machine learning. While neural networks are highly versatile and capable of learning complex patterns, they often lack interpretability due to their ``black box'' nature. On the other hand, probabilistic ``white box'' models, though interpretable, often suffer from a significant performance gap when compared to neural networks. To address this, we propose a novel quantum physics-based ``white box'' method that offers both accurate uncertainty quantification and enhanced interpretability. By mapping the kernel mean embedding (KME) of a time series data vector to a reproducing kernel Hilbert space (RKHS), we construct a tensor network-inspired 1D spin chain Hamiltonian, with the KME as one of its eigen-functions or eigen-modes. We then solve the associated Schr{ö}dinger equation and apply perturbation theory to quantify uncertainty, thereby improving the interpretability of tasks performed with the quantum tensor network-based model. We demonstrate the effectiveness of this methodology, compared to state-of-the-art ``white box" models, in change point detection and time series clustering, providing insights into the uncertainties associated with decision-making throughout the process.

Projection-based DMRG-in-DFT embedding corrected by non-additive exchange-correlation

Authors: Enzo Monino, Daria Drwal, Pavel Beran, Michał Hapka, Libor Veis, Katarzyna Pernal

arXiv ID: 2511.13346 | Date: 2025-11-17

Abstract: The projection-based wave function (WF)-in-DFT embedding enables an efficient description of both the energetics and properties of large and complex chemical systems, with accuracy exceeding that of pure DFT. Recently, we have proposed using the density matrix renormalization group (DMRG) as the WF method for molecules containing strongly correlated fragments [Beran, P. et al. J. Phys. Chem. Lett. 2023, 14, 3, 716-722]. In this work, we demonstrate that the accuracy of the DMRG-in-DFT approach is primarily limited by the approximate treatment of the coupling between the active component and its environment through nonadditive exchange-correlation functionals. To address this issue, we combine exact exchange to reduce the nonadditive exchange error with a multireference adiabatic connection (AC) scheme to recover nonadditive correlation. The performance of the improved DMRG-in-DFT embedding is illustrated on two prototypical strongly correlated systems: the dissociation of the H20 chain and the cleavage of a triple CN bond in propionitrile.

Numerical renormalization group integrated Hamiltonian truncation: Toward generic deformation of integrable lattice models

Authors: Xiaodong He, Xiao Wang, Jianda Wu

arXiv ID: 2511.13218 | Date: 2025-11-17

Abstract: We present a hybrid lattice Hamiltonian truncation method that integrates the numerical renormalization group (NRG) with a truncated lattice integrable spectrum. The technique is tailored for generic deformations of integrable lattice models, where the NRG enables a controlled incorporation of high-energy states. The method extends the basis set more effectively and efficiently than brute-force truncation, meanwhile significantly reducing errors. We show its capability on two paradigmatic models: an Ising chain in a magnetic field and a quantum Ising ladder. The resulting dynamical structure factors accurately capture the essential low-energy physics, including the E8E_8 and D8(1)\mathcal{D}_8^{(1)} excitations of the former and later models, respectively, demonstrating the approach's computational efficiency and high performance.

Measurement-Based Quantum Computation Using the Spin-1 XXZ Model with Uniaxial Anisotropy

Authors: Hiroki Ohta, Aaron Merlin Müller, Shunji Tsuchiya

arXiv ID: 2511.12000 | Date: 2025-11-15

Abstract: We demonstrate that the ground state of a spin-1 XXZ chain with uniaxial anisotropies, single-ion anisotropy DD and Ising-like anisotropy JJ, within the Haldane phase can serve as a resource state for measurement-based quantum computation implementing single-qubit gates. The gate fidelity of both elementary rotation gates and general single-qubit unitary gates composed of rotations about the xx-, yy-, and zz-axes is evaluated, and is found to exceed 0.99 when DD or JJ is appropriately tuned. Furthermore, we derive an analytic expression for the rotation-gate fidelity under the assumption that the state lies within the Z2×Z2\mathbb Z_2\times\mathbb Z_2-protected Haldane phase, showing that it is determined by the post-measurement spin-spin correlation function and the failure probability. The observed enhancement of gate fidelity in the spin-1 XXZ chain originates from the strengthening of antiferromagnetic (AFM) correlations near the AFM phase, which effectively suppresses failure states.

Fast and Expressive Multi-Token Prediction with Probabilistic Circuits

Authors: Andreas Grivas, Lorenzo Loconte, Emile van Krieken, Piotr Nawrot, Yu Zhao, Euan Wielewski, Pasquale Minervini, Edoardo Ponti, Antonio Vergari

arXiv ID: 2511.11346 | Date: 2025-11-14

Abstract: Multi-token prediction (MTP) is a prominent strategy to significantly speed up generation in large language models (LLMs), including byte-level LLMs, which are tokeniser-free but prohibitively slow. However, existing MTP methods often sacrifice expressiveness by assuming independence between future tokens. In this work, we investigate the trade-off between expressiveness and latency in MTP within the framework of probabilistic circuits (PCs). Our framework, named MTPC, allows one to explore different ways to encode the joint distributions over future tokens by selecting different circuit architectures, generalising classical models such as (hierarchical) mixture models, hidden Markov models and tensor networks. We show the efficacy of MTPC by retrofitting existing byte-level LLMs, such as EvaByte. Our experiments show that, when combined with speculative decoding, MTPC significantly speeds up generation compared to MTP with independence assumptions, while guaranteeing to retain the performance of the original verifier LLM. We also rigorously study the optimal trade-off between expressiveness and latency when exploring the possible parameterisations of MTPC, such as PC architectures and partial layer sharing between the verifier and draft LLMs.

Probing universal imaginary-time relaxation critical dynamics with infinite projected entangled pair states

Authors: He-Yu Lin, Shuai Yin, Z. Y. Xie, Zhong-Yi Lu

arXiv ID: 2511.10934 | Date: 2025-11-14

Abstract: We investigate the imaginary-time relaxation critical dynamics of the two-dimensional transverse-field Ising model using infinite projected entangled pair states (iPEPS) with the full-update strategy. Simulating directly in the thermodynamic limit, we explore the relaxation process near the critical point with two types of initial states: a fully polarized state and a product state with a small magnetization. For the fully polarized state, the magnetization shows a power law scaling Mτβ/(νz)M\propto τ^{-β/(νz)} in the imaginary-time evolution, from which both the critical point and critical exponent can be determined with high accuracy. For the nearly paramagnetic state, the relaxation process exhibits a behavior of MτθM\propto τ^θ with θ=0.1958θ=0.1958 being the critical initial-slip exponent, which is in good agreement with that obtained from the dynamic scaling of the self-correlation in quantum Monte Carlo method. These universal features emerge well before the system converges to the ground state, demonstrating the efficiency of imaginary-time evolution for probing quantum criticality. Our results demonstrate that iPEPS can serve as a robust and scalable method for studying dynamical critical phenomena in two-dimensional quantum many-body systems.

From One to Two Dimensions: Magnetic Phases in Weakly Coupled Spin Ladders

Authors: Mateo Cárdenes Wuttig, Andrew J. Millis

arXiv ID: 2511.10503 | Date: 2025-11-13

Abstract: A large variety of materials can be approximately described by means of spin-1/2 Heisenberg ladders. Here, the Density Matrix Renormalization Group (DMRG) algorithm together with a previously established numerical self-consistent mean-field approximation is used to investigate the magnetic properties of spin ladders coupled in a second dimension. The full ground state phase diagram including spin-gapped, antiferromagnetic, ferrimagnetic and fully polarized phases is presented as a function of interladder and intraladder coupling and magnetic field. Measurement of the dependence of magnetization on applied magnetic field is shown to enable location of a material on the phase diagram and determination of the Hamiltonian parameters. These results provide a practical route toward identifying and characterizing magnetic materials composed of coupled spin ladders.

Continuum limit of gauged tensor network states

Authors: Gertian Roose, Erez Zohar

arXiv ID: 2511.10189 | Date: 2025-11-13

Abstract: It is well known that all physically relevant states of gauge theories lie in the sectors of the Hilbert space which satisfy the Gauss law. On the lattice, the manifeslty gauge invariant subspace is known to be exactly spanned by gauged tensor networks. In this work, we demonstrate that the continuum limit of certain types of gauged tensor networks is well defined and leads to a new class of states that may be helpful for the non-perturbative study of gauge theories directly in the continuum.

The zipper condition for 44-tensors in two-dimensional topological order and the higher relative commutants of a subfactor arising from a commuting square

Authors: Yasuyuki Kawahigashi

arXiv ID: 2511.10080 | Date: 2025-11-13

Abstract: They recently study two-dimensional topological order in condensed matter physics in terms of tensor networks involving certain 3- and 4-tensors. Their 3-tensors satisfying the ``zipper condition'' play an important role there. We identify their 4-tensors with bi-unitary connections in Jones' subfactor theory in operator algebras with precise normalization constants. Then we prove that their tensors satisfying the zipper condition are the same as flat fields of strings in subfactor theory which correspond to elements in the higher relative commutants of the subfactor arising from the bi-unitary connection. This is what we expect, since the zipper condition is a kind of pentagon relations, but we clarify what conditions are exactly needed for this -- we do not need the flatness or the finite depth condition for the bi-unitary connection. We actually generalize their 4-tensors so that the four index sets of the 4-tensors can be all different and work on a ``half-version'' of the zipper condition.

SeQuant Framework for Symbolic and Numerical Tensor Algebra. I. Core Capabilities

Authors: Bimal Gaudel, Robert G. Adam, Ajay Melekamburath, Conner Masteran, Nakul Teke, Azam Besharatnik, Andreas Köhn, Edward F. Valeev

arXiv ID: 2511.09943 | Date: 2025-11-13

Abstract: SeQuant is an open-source library for symbolic algebra of tensors over commutative (scalar) and non-commutative (operator) rings. The key innovation supporting most of its functionality is a graph-theoretic tensor network (TN) canonicalizer that can handle tensor networks with symmetries faster than their standard group-theoretic counterparts. The TN canonicalizer is used for routine simplification of conventional tensor expressions, for optimizing application of Wick's theorem (used to canonicalize products of tensors over operator fields), and for manipulation of the intermediate representation leading to the numerical evaluation. Notable features of SeQuant include support for noncovariant tensor networks (which often arise from tensor decompositions) and for tensors with modes that depend parametrically on indices of other tensor modes (such dependencies between degrees of freedom are naturally viewed as nesting of tensors, "tensors of tensors" arising in block-wise data compressions in data science and modern quantum simulation). SeQuant blurs the line between pure symbolic manipulation/code generation and numerical evaluation by including compiler-like components to optimize and directly interpret tensor expressions using external numerical tensor algebra frameworks. The SeQuant source code is available at https://github.com/ValeevGroup/SeQuant.

Implicit Multiple Tensor Decomposition

Authors: Kunjing Yang, Libin Zheng, Minru Bai

arXiv ID: 2511.09916 | Date: 2025-11-13

Abstract: Recently, triple decomposition has attracted increasing attention for decomposing third-order tensors into three factor tensors. However, this approach is limited to third-order tensors and enforces uniformity in the lower dimensions across all factor tensors, which restricts its flexibility and applicability. To address these issues, we propose the Multiple decomposition, a novel framework that generalizes triple decomposition to arbitrary order tensors and allows the short dimensions of the factor tensors to differ. We establish its connections with other classical tensor decompositions. Furthermore, implicit neural representation (INR) is employed to continuously represent the factor tensors in Multiple decomposition, enabling the method to generalize to non-grid data. We refer to this INR-based Multiple decomposition as Implicit Multiple Tensor Decomposition (IMTD). Then, the Proximal Alternating Least Squares (PALS) algorithm is utilized to solve the IMTD-based tensor reconstruction models. Since the objective function in IMTD-based models often lacks the Kurdyka-Lojasiewicz (KL) property, we establish a KL-free convergence analysis for the algorithm. Finally, extensive numerical experiments further validate the effectiveness of the proposed method.

Accelerating two-dimensional tensor network optimization by preconditioning

Authors: Xing-Yu Zhang, Qi Yang, Philippe Corboz, Jutho Haegeman, Wei Tang

arXiv ID: 2511.09546 | Date: 2025-11-12

Abstract: We revisit gradient-based optimization for infinite projected entangled pair states (iPEPS), a tensor network ansatz for simulating many-body quantum systems. This approach is hindered by two major challenges: the high computational cost of evaluating energies and gradients, and an ill-conditioned optimization landscape that slows convergence. To reduce the number of optimization steps, we introduce an efficient preconditioner derived from the leading term of the metric tensor. We benchmark our method against standard optimization techniques on the Heisenberg and Kitaev models, demonstrating substantial improvements in overall computational efficiency. Our approach is broadly applicable across various contraction schemes, unit cell sizes, and Hamiltonians, highlighting the potential of preconditioned optimization to advance tensor network algorithms for strongly correlated systems.

A Tensor Residual Circuit Neural Network Factorized with Matrix Product Operation

Authors: Andi Chen

arXiv ID: 2511.09315 | Date: 2025-11-12

Abstract: It is challenging to reduce the complexity of neural networks while maintaining their generalization ability and robustness, especially for practical applications. Conventional solutions for this problem incorporate quantum-inspired neural networks with Kronecker products and hybrid tensor neural networks with MPO factorization and fully-connected layers. Nonetheless, the generalization power and robustness of the fully-connected layers are not as outstanding as circuit models in quantum computing. In this paper, we propose a novel tensor circuit neural network (TCNN) that takes advantage of the characteristics of tensor neural networks and residual circuit models to achieve generalization ability and robustness with low complexity. The proposed activation operation and parallelism of the circuit in complex number field improves its non-linearity and efficiency for feature learning. Moreover, since the feature information exists in the parameters in both the real and imaginary parts in TCNN, an information fusion layer is proposed for merging features stored in those parameters to enhance the generalization capability. Experimental results confirm that TCNN showcases more outstanding generalization and robustness with its average accuracies on various datasets 2\%-3\% higher than those of the state-of-the-art compared models. More significantly, while other models fail to learn features under noise parameter attacking, TCNN still showcases prominent learning capability owing to its ability to prevent gradient explosion. Furthermore, it is comparable to the compared models on the number of trainable parameters and the CPU running time. An ablation study also indicates the advantage of the activation operation, the parallelism architecture and the information fusion layer.

Infinite-component BFBF field theory: Nexus of fracton order, Toeplitz braiding, and non-Hermitian amplification

Authors: Bo-Xi Li, Peng Ye

arXiv ID: 2511.09301 | Date: 2025-11-12

Abstract: Building on the recent study of Toeplitz braiding by Li et al. [Phys. Rev. B 110, 205108 (2024)], we introduce \textit{infinite-component} BFBF (iBFBF) theories by stacking topological BFBF theories along a fourth (ww) spatial direction and coupling them in a translationally invariant manner. The iBFBF framework captures the low-energy physics of 4D fracton topological orders in which both particle and loop excitations exhibit restricted mobility along the stacking direction, and their particle-loop braiding statistics are encoded in asymmetric, integer-valued Toeplitz KK matrices. We identify a novel form of particle-loop braiding, termed \textit{Toeplitz braiding}, originating from boundary zero singular modes (ZSMs) of the KK matrix. In the thermodynamic limit, nontrivial braiding phases persist even when the particle and loop reside on opposite 3D boundaries, as the boundary ZSMs dominate the nonvanishing off-diagonal elements of K1K^{-1} and govern boundary-driven braiding behavior. Analytical and numerical studies of iBFBF theories with Hatano-Nelson-type and non-Hermitian Su-Schrieffer-Heeger-type Toeplitz KK matrices confirm the correspondence between ZSMs and Toeplitz braiding. The iBFBF construction thus forges a bridge between strongly correlated topological field theory and noninteracting non-Hermitian physics, where ZSMs underlie the non-Hermitian amplification effect. Possible extensions include 3-loop and Borromean-rings Toeplitz braiding induced by twisted topological terms, generalized entanglement renormalization, and foliation structures within iBFBF theories. An intriguing analogy to the scenario of parallel universes is also briefly discussed.

Tensor Network Framework for Forecasting Nonlinear and Chaotic Dynamics

Authors: Jia-Bin You, Jian Feng Kong, Jun Ye

arXiv ID: 2511.09233 | Date: 2025-11-12

Abstract: We present a tensor network model (TNM) for forecasting nonlinear and chaotic dynamics, bridging quantum many-body methods with classical complex systems. The TNM leverages hierarchical tensor contractions to encode non-Markovian temporal correlations and multiscale structures, enabling compact and interpretable representations of chaotic flows. Using the Lorenz and Rössler systems as benchmarks, we show that the TNM accurately reconstructs short-term trajectories and faithfully captures the attractor geometry. The model enables robust short-term forecasting beyond several Lyapunov times, offering a meaningful horizon for data-driven prediction under chaos. Inhomogeneous parametrization of weight tensors improves convergence and robustness compared to homogeneous parametrization, while scaling with bond dimension reveals saturation beyond modest values, consistent with the low intrinsic dimensionality of the chaotic attractor. This work establishes tensor networks as a universal paradigm for data-driven modeling of complex dynamical systems, offering physically motivated control of model expressivity and opening pathways toward applications in climate systems and hybrid quantum-classical simulations.

Evidence for spontaneous breaking of a continuous symmetry at a non-conformal quantum critical point in one dimension

Authors: R. Flores-Calderón, M. Zündel

arXiv ID: 2511.09097 | Date: 2025-11-12

Abstract: In this work, we present evidence for the spontaneous breaking of a continuous symmetry in a nearest-neighbour interacting spin-1 chain tuned to a quantum critical point at T=0T=0 between two XY quasi-long-range order phases differing by the spontaneous breaking of a Z2\mathbb{Z}_2 symmetry. Despite the one-dimensional nature of the system, which typically prevents such a continuous symmetry breaking due to the Hohenberg-Mermin-Wagner theorem, the presence of a Berry phase term in the quantum model allows us to observe, using matrix product state methods, a finite perpendicular magnetization. Moreover, the quasi-long-range decay of the correlation function becomes truly long-range order, and the dynamical structure factor displays a characteristic Bragg peak together with sharp gapless modes. Our results imply the quantum phase transition has an anomalous dimension of η1η\simeq 1 together with the dynamical critical exponent z3/2z\simeq 3/2, known from the Kardar-Parisi-Zhang universality class in one dimension. We perform a perturbative renormalization group calculation about the upper critical dimension dc=2d_c=2 that we could close at second loop order. We find an interacting fixed point with critical exponents distinct from the Ising ones. Together, our findings suggest the nature of the fixed point to be non-perturbative. We propose a field-theory that we believe to improve the quantitative results.

Exact Floquet dynamics of strongly damped driven quantum systems

Authors: Konrad Mickiewicz, Valentin Link, Walter T. Strunz

arXiv ID: 2511.08754 | Date: 2025-11-11

Abstract: We present an approach for efficiently simulating strongly damped quantum systems subjected to periodic driving, employing a periodic matrix product operator representation of the influence functional. This representation enables the construction of a numerically exact Floquet propagator that captures the non-Markovian open system dynamics, thus providing a dissipative analogue to the Floquet Hamiltonian of driven isolated quantum systems. We apply this method to study the asymptotic heating of a reservoir in spin-boson models, characterizing the deviation from equilibrium conditions. Moreover, we show how a local driving of two qubits can be utilized to stabilize a transient entanglement buildup of the qubits originating from the interaction with a common environment. Our results make it possible to directly study both stationary and transient dynamics of strongly damped and driven quantum systems within a transparent theoretical and numerical framework.

Exploring the performance of superposition of product states: from 1D to 3D quantum spin systems

Authors: Apimuk Sornsaeng, Itai Arad, Dario Poletti

arXiv ID: 2511.08407 | Date: 2025-11-11

Abstract: Tensor networks (TNs) are one of the best available tools to study many-body quantum systems. TNs are particularly suitable for one-dimensional local Hamiltonians, while their performance for generic geometries is mainly limited by two aspects: the limitation in expressive power and the approximate extraction of information. Here we investigate the performance of superposition-of-product-states (SPS) ansatz, a variational framework structurally related to canonical polyadic tensor decomposition. The ansatz does not compress information as effectively as tensor networks, but it has the advantages (i) of allowing accurate extraction of information, (ii) of being structurally independent of the geometry of the system, (iii) of being readily parallelizable, and (iv) of allowing analytical shortcuts. We first study the typical properties of the SPS ansatz for spin-1/21/2 systems, including its entanglement entropy, and its trainability. We then use this ansatz for ground state search in tilted Ising models -- including one-dimensional and three-dimensional with short- and long-range interaction, and a random network -- demonstrating that SPS can attain high accuracy.

Multistart Large Neighborhood Search for the liquefied natural gas transportation and trading over long-term time horizons

Authors: S. Iudin, M. Veshchezerova, K. Tsarova, G. Tadumadze, V. Shete, J. -K. Hao, M. Perelshtein

arXiv ID: 2511.08404 | Date: 2025-11-11

Abstract: Liquefied Natural Gas (LNG) transportation is a critical component of the energy industry. It enables the efficient and large-scale movement of natural gas across vast distances by converting it into a liquid form, thereby addressing global demand and connecting suppliers with consumers. In this study, we present the Multistart Large Neighborhood Search heuristic for the LNG transportation problem, which involves hundreds of contracts and a planning horizon of two to three years. Our model incorporates several fuel types, LNG sloshing in the tank, and speed- and load-dependent consumption rates. We also consider flexible contracts with LNG volume variability, enabling volume optimizations and multiple discharges. A tensor-train optimizer defines the parameters of Mixed Integer Programming (MIP) models, allowing better solution space exploration. On the historic and artificially generated data, our approach outperforms the baseline linear-programming model by 35% and 44%, respectively, while the time overhead is only several minutes.

Local spreading of stabilizer Rényi entropy in a brickwork random Clifford circuit

Authors: Somnath Maity, Ryusuke Hamazaki

arXiv ID: 2511.07769 | Date: 2025-11-11

Abstract: Nonstabilizerness, or magic, constitutes a fundamental resource for quantum computation and a crucial ingredient for quantum advantage. Recent progress has substantially advanced the characterization of magic in many-body quantum systems, with stabilizer Rényi entropy (SRE) emerging as a computable and experimentally accessible measure. In this work, we investigate the spreading of SRE in terms of single-qubit reduced density matrices, where an initial product state that contains magic in a local region evolves under brickwork random Clifford circuits. For the case with Haar-random local Clifford gates, we find that the spreading profile exhibits a diffusive structure within a ballistic light cone when viewed through a normalized version of single-qubit SRE, despite the absence of explicit conserved charges. We further examine the robustness of this non-ballistic behavior of the normalized single-qubit SRE spreading by extending the analysis to a restricted Clifford circuit, where we unveil a superdiffusive spreading.

Topological and Trivial Valence-Bond Orders in Higher-Spin Kitaev Models

Authors: Xing-Yu Zhang, Qi Yang, Philippe Corboz, Jutho Haegeman, Yuchi He

arXiv ID: 2511.07415 | Date: 2025-11-10

Abstract: We investigate the quantum phases of higher-spin Kitaev models using tensor network methods. Our results reveal distinct bond-ordered phases for spin-1, spin-32\tfrac{3}{2}, and spin-2 models. In all cases, we find translational symmetry breaking with unit cells being tripled by forming valence-bond orders. However, these three phases are distinct, forming plaquette order, topological dimer order, and non-topological dimer order, respectively. Our findings are based on a cross-validation between variational two-dimensional tensor network calculations: an unrestricted exploration of symmetry-broken states versus the detection of symmetry breaking from cat-state behavior in symmetry-restricted states. The origin of different orders can also be understood from a theoretical analysis. Our work sheds light upon the interplay between topological and symmetry-breaking orders as well as their detection via tensor networks.

Characterizing Mott Insulators in the Interacting One-Body Picture

Authors: Theo N. Dionne, Santiago Villodre, Mikel Iraola, Maia G. Vergniory

arXiv ID: 2511.07331 | Date: 2025-11-10

Abstract: We present a framework to characterize Mott insulating phases within the interacting one-body picture, focusing on the Hubbard diamond chain featuring both Hubbard interactions and spin-orbit coupling simulated within cellular dynamical mean field theory. Using symmetry analysis of the single-particle Green's function, we classify spectral functions by irreducible representations at high-symmetry points of the Brillouin zone. Complementarily, we calculate the one-body reduced density matrix which allows us to reach both a qualitative description of charge distribution and an analysis of the state purity. Moreover, within the Tensor Network framework, we employ a Density Matrix Renormalization Group approach to confirm the presence of three distinct phases and their corresponding phase transitions. Our results highlight how symmetry-labelled spectral functions and effective orbital analysis provide accessible single-particle tools for probing correlation-driven insulating phases.

Thermal Tensor Network Simulations of Fermions with a Fixed Filling

Authors: Qiaoyi Li, Dai-Wei Qu, Bin-Bin Chen, Tao Shi, Wei Li

arXiv ID: 2511.07303 | Date: 2025-11-10

Abstract: Numerical simulations of strongly correlated fermions at finite temperature are essential for studying high-temperature superconductivity and other quantum many-body phenomena. The recently developed tangent-space tensor renormalization group (tanTRG) provides an efficient and accurate framework by representing thermal density operators as matrix product operators. However, the particle number generally varies during the cooling process. The conventional strategy of fine-tuning chemical potentials to reach a target filling is computationally demanding. Here we propose a fixed-NN tanTRG algorithm that stabilizes the average particle number by adaptively tuning the chemical potential within the imaginary-time evolution. We benchmark its accuracy on exactly solvable free fermions, and further apply it to the square-lattice Hubbard model. For hole-doped cases, we study the temperature evolution of charge and spin correlations, identifying several characteristic temperature scales for stripe formation. Our results establish fixed-NN tanTRG as an efficient and reliable tool for finite-temperature studies of correlated fermion systems.

Matrix-product state skeletons in Onsager-integrable quantum chains

Authors: Imogen Camp, Nick G. Jones

arXiv ID: 2511.07212 | Date: 2025-11-10

Abstract: Matrix-product state (MPS) skeletons are connected networks of Hamiltonians with exact MPS ground states that underlie a phase diagram. Such skeletons have previously been found in classes of free-fermion models. For the translation-invariant BDI and AIII free-fermion classes, it has been shown that the underlying skeleton is dense, giving an analytic approach to MPS approximation of ground states anywhere in the class. In this paper, we partially expose the skeleton in certain interacting spin chains: the NN-state Onsager-integrable chiral clock families. We construct MPS that form a dense MPS skeleton in the gapped regions surrounding a sequence of fixed-point Hamiltonians (the generators of the Onsager algebra). Outside these gapped regions, these MPS remain eigenstates, but no longer give the many-body ground state. Rather, they are ground states in particular sectors of the spectrum. Our methods also allow us to find further MPS eigenstates; these correspond to low-lying excited states within the aforementioned gapped regions. This set of MPS excited states goes beyond the previous analysis of ground states on the N=2N=2 free-fermion MPS skeleton. As an application of our results, we find a closed form for the disorder parameter in a family of interacting models. Finally, we remark that many of our results use only the Onsager algebra and are not specific to the chiral clock model representation.

Optimal phase estimation in the presence of correlated dephasing

Authors: Srijon Ghosh, Arkadiusz Kobus, Stanisław Kurdziałek, Rafał Demkowicz-Dobrzański

arXiv ID: 2511.07211 | Date: 2025-11-10

Abstract: We investigate optimal metrological protocols for phase estimation in the presence of correlated dephasing noise, including spin-squeezed states sensing strategies as well as parallel and adaptive protocols optimized using tensor-network based numerical methods. The results are benchmarked against fundamental bounds obtained either via a latest quantum comb extension method or an optimized classical simulation method. We find that the spin-squeezed offer practically optimal performance in the regime where phase fluctuations are positively correlated, but can be outperformed by tensor-network optimized strategies for negatively correlated fluctuations.

GCAMPS: A Scalable Classical Simulator for Qudit Systems

Authors: Ben Harper, Azar C. Nakhl, Thomas Quella, Martin Sevior, Muhammad Usman

arXiv ID: 2511.06672 | Date: 2025-11-10

Abstract: Classical simulations of quantum systems are notoriously difficult computational problems, with conventional state vector and tensor network methods restricted to quantum systems that feature only a small number of qudits. The recently introduced Clifford Augmented Matrix Product State (CAMPS) method offer scalability and efficiency by combining both tensor network and stabilizer simulation techniques and leveraging their complementary advantages. This hybrid simulation method has indeed demonstrated significant improvements in simulation performance for qubit circuits. Our work generalises the CAMPS method to higher quantum degrees of freedom -- qudit simulation, resulting in a generalised CAMPS (GCAMPS). Benchmarking this extended simulator on quantum systems with three degrees of freedom, i.e. qutrits, we show that similar to the case of qubits, qutrit systems also benefit from a comparable speedup using these techniques. Indeed, we see a greater improvement with qutrit simulation compared to qubit simulation on the same TT-doped random Clifford benchmarking circuit as a result of the increased difficulty of conventional qutrit simulation using tensor networks. This extension allows for the classical simulation of problems that were previously intractable without access to a quantum device and will open new avenues to study complex many-body physics and to develop efficient methods for quantum information processing.

Efficient Approximation of Volterra Series for High-Dimensional Systems

Authors: Navin Khoshnan, Claudia K Petritsch, Bryce-Allen Bagley

arXiv ID: 2511.06527 | Date: 2025-11-09

Abstract: The identification of high-dimensional nonlinear dynamical systems via the Volterra series has significant potential, but has been severely hindered by the curse of dimensionality. Tensor Network (TN) methods such as the Modified Alternating Linear Scheme (MVMALS) have been a breakthrough for the field, offering a tractable approach by exploiting the low-rank structure in Volterra kernels. However, these techniques still encounter prohibitive computational and memory bottlenecks due to high-order polynomial scaling with respect to input dimension. To overcome this barrier, we introduce the Tensor Head Averaging (THA) algorithm, which significantly reduces complexity by constructing an ensemble of localized MVMALS models trained on small subsets of the input space. In this paper, we present a theoretical foundation for the THA algorithm. We establish observable, finite-sample bounds on the error between the THA ensemble and a full MVMALS model, and we derive an exact decomposition of the squared error. This decomposition is used to analyze the manner in which subset models implicitly compensate for omitted dynamics. We quantify this effect, and prove that correlation between the included and omitted dynamics creates an optimization incentive which drives THA's performance toward accuracy superior to a simple truncation of a full MVMALS model. THA thus offers a scalable and theoretically grounded approach for identifying previously intractable high-dimensional systems.

Phase transitions in the spin-1/2 Heisenberg antiferromagnet on the square lattice

Authors: Jie Qiao, Shu-Hao Zhang, Jing-Bo Qin, Xiao-Long Zhao, Qiang Cheng

arXiv ID: 2511.06423 | Date: 2025-11-09

Abstract: The nature of the intermediate ground-state phase in the spin-1/2 frustrated square lattice model has long been debated. Using cluster density matrix embedding theory, we investigate the phase diagram of this model. The Neel phase is directly identified for J2<0.45 and the collinear phase for J2>0.65 based on the ground state. Although no direct evidence of an internal phase transition is found within the intermediate phase from the ground state, analysis of the first excited state wave function reveals a continuous quantum phase transition in this region, with a critical point at J2=0.55. This critical point divides the intermediate phase into PVBS and CVBS.

Simulating Clifford Circuits with Gaussian Elimination

Authors: Yuchen Pang, Edgar Solomonik

arXiv ID: 2511.06127 | Date: 2025-11-08

Abstract: Quantum circuits are considered more powerful than classical circuits and require exponential resources to simulate classically. Clifford circuits are a special class of quantum circuits that can be simulated in polynomial time but still show important quantum effects such as entanglement. In this work, we present an algorithm that simulates Clifford circuits by performing Gaussian elimination on a modified adjacency matrix derived from the circuit structure. Our work builds on an ZX-calculus tensor network representation of Clifford circuits that reduces to quantum graph states. We give a concise formula of amplitudes of graph states based on the LDL decomposition of matrices over GF(2), and use it to get efficient algorithms for strong and weak simulation of Clifford circuits using tree-decomposition-based fast LDL algorithm. The complexity of our algorithm matches the state of art for weak graph state simulation and improves the state of art for strong graph state simulation by taking advantage of Strassen-like fast matrix multiplication. Our algorithm is also efficient when computing many amplitudes or samples of a Clifford circuit. Further, our amplitudes formula provides a new characterization of locally Clifford equivalent graph states as well as an efficient protocol to learn graph states with low-rank adjacency matrices.

Beyond Penrose tensor diagrams with the ZX calculus: Applications to quantum computing, quantum machine learning, condensed matter physics, and quantum gravity

Authors: Quanlong Wang, Richard D. P. East, Razin A. Shaikh, Lia Yeh, Boldizsár Poór, Bob Coecke

arXiv ID: 2511.06012 | Date: 2025-11-08

Abstract: We introduce the Spin-ZX calculus as an elevation of Penrose's diagrams and associated binor calculus to the level of a formal diagrammatic language. The power of doing so is illustrated by the variety of scientific areas we apply it to: permutational quantum computing, quantum machine learning, condensed matter physics, and quantum gravity. Respectively, we analyse permutational computing transition amplitudes, evaluate barren plateaus for SU(2) symmetric ansätze, study properties of AKLT states, and derive the minimum quantised volume in loop quantum gravity. Our starting point is the mixed-dimensional ZX calculus, a purely diagrammatic language that has been proven to be complete for finite-dimensional Hilbert spaces. That is, any equation that can be derived in the Hilbert space formalism, can also be derived in the mixed-dimensional ZX calculus. We embed the Spin-ZX calculus inside the mixed-dimensional ZX calculus, rendering it a quantum information flavoured diagrammatic language for the quantum theory of angular momentum, i.e. SU(2) representation theory. We diagrammatically derive the fundamental spin coupling objects - such as Clebsch-Gordan coefficients, symmetrising mappings between qubits and spin spaces, and spin Hamiltonians - under this embedding. Our results establish the Spin-ZX calculus as a powerful tool for representing and computing with SU(2) systems graphically, offering new insights into foundational relationships and paving the way for new diagrammatic algorithms for theoretical physics.

Color code thresholds under circuit-level noise beyond the Pauli framework

Authors: Francesco Pio Barone, Daniel Jaschke, Ilaria Siloi, Simone Montangero

arXiv ID: 2511.05719 | Date: 2025-11-07

Abstract: A quantum error correction code is assessed over its ability to correct errors in noisy quantum circuits. This task requires extensive simulations of faulty quantum circuits, which are often made tractable by considering stochastic Pauli noise models, as they are compatible with efficient classical simulation techniques. However, such noise models do not fully capture the variety of physical error mechanisms encountered in realistic quantum platforms. In this work, we extend circuit-level noise modeling beyond the Pauli framework by estimating the threshold of the color code under more general noise models. Specifically, we consider two representative non-Pauli error channels: a systematic XX-rotation model that introduces coherent over-rotations, and an amplitude damping channel that captures relaxation processes. These models are incorporated at the circuit level into color code circuits using a Tree Tensor Network ansatz. Our simulations demonstrate that tensor network simulations enable accurate threshold estimation under non-Pauli noise for color codes up to distance d=7d=7 (73 qubits). Comparing our results with the Pauli twirling approximations of the noise models, we find that coherent over-rotations yield systematically higher error rates, deviating from the Pauli twirling approximation as the code distance increases.

Quantum Data Representation via Circuit Partitioning and Reintegration

Authors: Ziqing Guo, Jan Balewski, Kewen Xiao, Ziwen Pan

arXiv ID: 2511.05492 | Date: 2025-11-07

Abstract: Quantum data encoding (QDE) enables faster com-putations than classical algorithms through superposition and en-tanglement. Circuit cutting and knitting are effective techniques for ameliorating current noisy quantum processing unit (QPUs) errors via a divide-and-conquer approach that splits quantum circuits into subcircuits and recombines them using classical postprocessing. Unfortunately, the existing QDE frameworks fail to consider quantum hardware limitations, such as the topology of the chip. Designing a computation model that supports the algorithm level of quantum computation and optimizes non-all-to-all connected quantum circuit simulations remains underde-veloped. In this study, we introduce shardQ, a method that leverages the SparseCut algorithm with matrix product state (MPS) compilation and a global knitting technique to mitigate the quantum error rates. This method elucidates the optimal trade-off between the computational time and error rate for quantum encoding with a theoretical proof, evidenced by an ablation analysis using an IBM Heron-type QPUs with 15% error reduction. This study also presents the results of quantum image encoding readiness. The proposed model advances the current quantum computation towards the fault-tolerant regime as QDE is the input of grand unified quantum algorithms.

Exact strong zero modes in quantum circuits and spin chains with non-diagonal boundary conditions

Authors: Sascha Gehrmann, Fabian H. L. Essler

arXiv ID: 2511.05490 | Date: 2025-11-07

Abstract: We construct exact strong zero mode operators (ESZM) in integrable quantum circuits and the spin-1/2 XXZ chain for general open boundary conditions, which break the bulk U(1) symmetry of the time evolution operators. We show that the ESZM is localized around one of the boundaries and induces infinite boundary coherence times. Finally, we prove that the ESZM becomes spatially non-local under the map that relates the spin-1/2 XXZ chain to the asymmetric simple exclusion process, which suggests that it does not play a significant role in the dynamics of the latter.

TT-Edge: A Hardware-Software Co-Design for Energy-Efficient Tensor-Train Decomposition on Edge AI

Authors: Hyunseok Kwak, Kyeongwon Lee, Kyeongpil Min, Chaebin Jung, Woojoo Lee

arXiv ID: 2511.13738 | Date: 2025-11-07

Abstract: The growing demands of distributed learning on resource constrained edge devices underscore the importance of efficient on device model compression. Tensor Train Decomposition (TTD) offers high compression ratios with minimal accuracy loss, yet repeated singular value decompositions (SVDs) and matrix multiplications can impose significant latency and energy costs on low power processors. In this work, we present TT-Edge, a hardware software co designed framework aimed at overcoming these challenges. By splitting SVD into two phases--bidiagonalization and diagonalization--TT-Edge offloads the most compute intensive tasks to a specialized TTD Engine. This engine integrates tightly with an existing GEMM accelerator, thereby curtailing the frequent matrix vector transfers that often undermine system performance and energy efficiency. Implemented on a RISC-V-based edge AI processor, TT-Edge achieves a 1.7x speedup compared to a GEMM only baseline when compressing a ResNet 32 model via TTD, while reducing overall energy usage by 40.2 percent. These gains come with only a 4 percent increase in total power and minimal hardware overhead, enabled by a lightweight design that reuses GEMM resources and employs a shared floating point unit. Our experimental results on both FPGA prototypes and post-synthesis power analysis at 45 nm demonstrate that TT-Edge effectively addresses the latency and energy bottlenecks of TTD based compression in edge environments.

XYZ integrability the easy way

Authors: Paul Fendley, Sascha Gehrmann, Eric Vernier, Frank Verstraete

arXiv ID: 2511.04674 | Date: 2025-11-06

Abstract: Sutherland showed that the XYZ quantum spin-chain Hamiltonian commutes with the eight-vertex model transfer matrix, so that Baxter's subsequent tour de force proves the integrability of both. The proof requires parametrising the Boltzmann weights using elliptic theta functions and showing they satisfy the Yang-Baxter equation. We here give a simpler derivation of the integrability of the XYZ chain by explicitly constructing an extensive sequence of conserved charges from a matrix-product operator. We show that they commute with the XYZ Hamiltonian with periodic boundary conditions or an arbitrary boundary magnetic field. A straightforward generalisation yields impurity interactions that preserve the integrability. Placing such an impurity at the edge gives an integrable generalisation of the Kondo problem with a gapped bulk. We make contact with the traditional approach by relating our matrix-product operator to products of the eight-vertex model transfer matrix.

Continuous matrix product operators for quantum fields

Authors: Erickson Tjoa, J. Ignacio Cirac

arXiv ID: 2511.04545 | Date: 2025-11-06

Abstract: In this work we introduce an ansatz for continuous matrix product operators for quantum field theory. We show that (i) they admit a closed-form expression in terms of finite number of matrix-valued functions without reference to any lattice parameter; (ii) they are obtained as a suitable continuum limit of matrix product operators; (iii) they preserve the entanglement area law directly in the continuum, and in particular they map continuous matrix product states (cMPS) to another cMPS. As an application, we use this ansatz to construct several families of continuous matrix product unitaries beyond quantum cellular automata.

Normalized tensor train decomposition

Authors: Renfeng Peng, Chengkai Zhu, Bin Gao, Xin Wang, Ya-xiang Yuan

arXiv ID: 2511.04369 | Date: 2025-11-06

Abstract: Tensors with unit Frobenius norm are fundamental objects in many fields, including scientific computing and quantum physics, which are able to represent normalized eigenvectors and pure quantum states. While the tensor train decomposition provides a powerful low-rank format for tackling high-dimensional problems, it does not intrinsically enforce the unit-norm constraint. To address this, we introduce the normalized tensor train (NTT) decomposition, which aims to approximate a tensor by unit-norm tensors in tensor train format. The low-rank structure of NTT decomposition not only saves storage and computational cost but also preserves the underlying unit-norm structure. We prove that the set of fixed-rank NTT tensors forms a smooth manifold, and the corresponding Riemannian geometry is derived, paving the way for geometric methods. We propose NTT-based methods for low-rank tensor recovery, high-dimensional eigenvalue problem, estimation of stabilizer rank, and calculation of the minimum output Rényi 2-entropy of quantum channels. Numerical experiments demonstrate the superior efficiency and scalability of the proposed NTT-based methods.

Unified Effective Field Theory for Nonlinear and Quantum Optics

Authors: Xiaochen Liu, Ken-Tye Yong

arXiv ID: 2511.04118 | Date: 2025-11-06

Abstract: Predicting phenomena that mix few-photon quantum optics with strong field nonlinear optics is hindered by the use of separate theoretical formalisms for each regime. We close this gap with a unified effective field theory valid for frequencies lower than the material-dependent cutoff set by the band gap, plasma frequency, or similar scale. The action couples the electromagnetic gauge field to vector polarisation modes. An isotropic potential generates the optical susceptibilities, while a higher-dimension axion-like term captures magnetoelectric effects; quantisation on the Schwinger-Keldysh contour with doubled BRST ghosts preserves gauge symmetry in dissipative media. One-loop renormalisation-group equations reproduce the measured dispersion of the third-order susceptibility from terahertz to near-visible frequencies after matching a single datum per material. Real-time dynamics solved with a matrix-product-operator engine yield good agreement with published results for GaAs polariton cavities, epsilon-near-zero indium-tin-oxide films and superconducting quarton circuits. The current formulation is limited to these 1-D geometries and sub-cut-off frequencies; higher-dimensional or above-cut-off phenomena will require additional degrees of freedom or numerical methods.

N-Mode Quantized Anharmonic Vibronic Hamiltonians for Matrix Product State Dynamics

Authors: Valentin Barandun, Nina Glaser, Markus Reiher

arXiv ID: 2511.03936 | Date: 2025-11-06

Abstract: Theoretical predictions of photochemical processes are essential for interpreting and understanding spectral features. Reliable quantum dynamics calculations of vibronic systems require precise modeling of anharmonic effects in the potential energy surfaces and off-diagonal nonadiabatic coupling terms. In this work, we present the n-mode quantization of all vibronic Hamiltonian terms comprised of general high-dimensional model representations. This results in a second-quantized framework for accurate vibronic calculations employing the density matrix renormalization group algorithm. We demonstrate the accuracy and reliability of this approach by calculating the excited state quantum dynamics of maleimide. We analyze convergence and the choice of parameters of the underlying time-dependent density matrix renormalization group algorithm for the n-mode vibronic Hamiltonian, demonstrating that it enables accurate calculations of complex photochemical dynamics.

Adaptive Randomized Tensor Train Rounding using Khatri-Rao Products

Authors: Hussam Al Daas, Grey Ballard, Laura Grigori, Mariana Martinez Aguilar, Arvind K. Saibaba, Bhisham Dev Verma

arXiv ID: 2511.03598 | Date: 2025-11-05

Abstract: Approximating a tensor in the tensor train (TT) format has many important applications in scientific computing. Rounding a TT tensor involves further compressing a tensor that is already in the TT format. This paper proposes new randomized algorithms for TT-rounding that uses sketches based on Khatri-Rao products (KRP). When the TT-ranks are known in advance, the proposed methods are comparable in cost to the sketches that used a sketching matrix in the TT-format~\cite{al2023randomized}. However, the use of KRP sketches enables adaptive algorithms to round the tensor in the TT-format within a fixed user-specified tolerance. An important component of the adaptivity is the estimation of error using KRP sketching, for which we develop theoretical guarantees. We report numerical experiments on synthetic tensors, parametric low-rank kernel approximations, and the solution of parametric partial differential equations. The numerical experiments show that we obtain speed-ups of up to 50×50\times compared to deterministic TT-rounding. Both the computational cost analysis and numerical experiments verify that the adaptive algorithms are competitive with the fixed rank algorithms, suggesting the adaptivity introduces only a low overhead.

LoRA-Edge: Tensor-Train-Assisted LoRA for Practical CNN Fine-Tuning on Edge Devices

Authors: Hyunseok Kwak, Kyeongwon Lee, Jae-Jin Lee, Woojoo Lee

arXiv ID: 2511.03765 | Date: 2025-11-05

Abstract: On-device fine-tuning of CNNs is essential to withstand domain shift in edge applications such as Human Activity Recognition (HAR), yet full fine-tuning is infeasible under strict memory, compute, and energy budgets. We present LoRA-Edge, a parameter-efficient fine-tuning (PEFT) method that builds on Low-Rank Adaptation (LoRA) with tensor-train assistance. LoRA-Edge (i) applies Tensor-Train Singular Value Decomposition (TT-SVD) to pre-trained convolutional layers, (ii) selectively updates only the output-side core with zero-initialization to keep the auxiliary path inactive at the start, and (iii) fuses the update back into dense kernels, leaving inference cost unchanged. This design preserves convolutional structure and reduces the number of trainable parameters by up to two orders of magnitude compared to full fine-tuning. Across diverse HAR datasets and CNN backbones, LoRA-Edge achieves accuracy within 4.7% of full fine-tuning while updating at most 1.49% of parameters, consistently outperforming prior parameter-efficient baselines under similar budgets. On a Jetson Orin Nano, TT-SVD initialization and selective-core training yield 1.4-3.8x faster convergence to target F1. LoRA-Edge thus makes structure-aligned, parameter-efficient on-device CNN adaptation practical for edge platforms.

Parametric Hierarchical Matrix Approximations to Kernel Matrices

Authors: Abraham Khan, Chao Chen, Vishwas Rao, Arvind K. Saibaba

arXiv ID: 2511.03109 | Date: 2025-11-05

Abstract: Kernel matrices are ubiquitous in computational mathematics, often arising from applications in machine learning and scientific computing. In two or three spatial or feature dimensions, such problems can be approximated efficiently by a class of matrices known as hierarchical matrices. A hierarchical matrix consists of a hierarchy of small near-field blocks (or sub-matrices) stored in a dense format and large far-field blocks approximated by low-rank matrices. Standard methods for forming hierarchical matrices do not account for the fact that kernel matrices depend on specific hyperparameters; for example, in the context of Gaussian processes, hyperparameters must be optimized over a fixed parameter space. We introduce a new class of hierarchical matrices, namely, parametric (parameter-dependent) hierarchical matrices. Members of this new class are parametric H\mathcal{H}-matrices and parametric H2\mathcal{H}^{2}-matrices. The construction of a parametric hierarchical matrix follows an offline-online paradigm. In the offline stage, the near-field and far-field blocks are approximated by using polynomial approximation and tensor compression. In the online stage, for a particular hyperparameter, the parametric hierarchical matrix is instantiated efficiently as a standard hierarchical matrix. The asymptotic costs for storage and computation in the offline stage are comparable to the corresponding standard approaches of forming a hierarchical matrix. However, the online stage of our approach requires no new kernel evaluations, and the far-field blocks can be computed more efficiently than standard approaches. {Numerical experiments show over 100×100\times speedups compared with existing techniques.}

SWAP-Network Routing and Spectral Qubit Ordering for MPS Imaginary-Time Optimization

Authors: Erik M. Åsgrim, Stefano Markidis

arXiv ID: 2511.02980 | Date: 2025-11-04

Abstract: We propose a quantum-inspired combinatorial solver that performs imaginary-time evolution (ITE) on a matrix product state (MPS), incorporating non-local couplings through structured SWAP networks and spectral qubit mapping of logical qubits. The SWAP networks, composed exclusively of local two-qubit gates, effectively mediate non-local qubit interactions. We investigate two distinct network architectures based on rectangular and triangular meshes of SWAP gates and analyze their performance in combination with spectral qubit ordering, which maps logical qubits to MPS sites based on the Laplacian of the logical qubit connectivity graph. The proposed framework is evaluated on synthetic MaxCut instances with varying graph connectivity, as well as on a dynamic portfolio optimization problem based on real historical asset data involving 180 qubits. On certain problem configurations, we observe an over 20×\times reduction in error when combining spectral ordering and triangular SWAP networks compared to optimization with shuffled qubit ordering. Furthermore, an analysis of the entanglement entropy during portfolio optimization reveals that spectral qubit ordering not only improves solution quality but also enhances the total and spatially distributed entanglement within the MPS. These findings demonstrate that exploiting problem structure through spectral mapping and efficient routing networks can substantially enhance the performance of tensor-network-based optimization algorithms.

Majorana string simulation of nonequilibrium dynamics in two-dimensional lattice fermion systems

Authors: Matteo D'Anna, Jannes Nys, Juan Carrasquilla

arXiv ID: 2511.02809 | Date: 2025-11-04

Abstract: The study of real-time dynamics of fermions remains one of the last frontiers beyond the reach of classical simulations and is key to our understanding of quantum behavior in chemistry and materials, with implications for quantum technology. Here we introduce a Heisenberg-picture algorithm that propagates observables expressed in a Majorana-string basis using a truncation scheme that preserves Trotter accuracy and aims at maintaining computational efficiency. The framework is exact for quadratic Hamiltonians--remaining restricted to a fixed low-weight sector determined by the physical observable--admits variational initial states, and can be extended to interacting regimes via systematically controlled truncations. We benchmark our approach on one- and two-dimensional Fermi-Hubbard quenches, comparing against tensor network methods (MPS and fPEPS) and recent experimental data. The method achieves high accuracy on timescales comparable to state-of-the-art variational techniques and experiments, demonstrating that controlled Majorana-string truncation is a practical tool for simulating two-dimensional fermionic dynamics.

The Born Ultimatum: Conditions for Classical Surrogation of Quantum Generative Models with Correlators

Authors: Mario Herrero-Gonzalez, Brian Coyle, Kieran McDowall, Ross Grassie, Sjoerd Beentjes, Ava Khamseh, Elham Kashefi

arXiv ID: 2511.01845 | Date: 2025-11-03

Abstract: Quantum Circuit Born Machines (QCBMs) are powerful quantum generative models that sample according to the Born rule, with complexity-theoretic evidence suggesting potential quantum advantages for generative tasks. Here, we identify QCBMs as a quantum Fourier model independently of the loss function. This allows us to apply known dequantization conditions when the optimal quantum distribution is available. However, realizing this distribution is hindered by trainability issues such as vanishing gradients on quantum hardware. Recent train-classical, deploy-quantum approaches propose training classical surrogates of QCBMs and using quantum devices only for inference. We analyze the limitations of these methods arising from deployment discrepancies between classically trained and quantumly deployed parameters. Using the Fourier decomposition of the Born rule in terms of correlators, we quantify this discrepancy analytically. Approximating the decomposition via distribution truncation and classical surrogation provides concrete examples of such discrepancies, which we demonstrate numerically. We study this effect using tensor-networks and Pauli-propagation-based classical surrogates. Our study examines the use of IQP circuits, matchcircuits, Heisenberg-chain circuits, and Haldane-chain circuits for the QCBM ansatz. In doing so, we derive closed-form expressions for Pauli propagation in IQP circuits and the dynamical Lie algebra of the Haldane chain, which may be of independent interest.

Superconductivity of bilayer two-orbital Hubbard model for La3_{3}Ni2_{2}O7_{7} under high pressure

Authors: Wei-Yang Chen, Cui-Qun Chen, Meng Wang, Shou-Shu Gong, Dao-Xin Yao

arXiv ID: 2511.01801 | Date: 2025-11-03

Abstract: By combining density functional theory (DFT) and density matrix renormalization group calculations, we investigate the unusual pressure dependence of superconducting transition temperature (TcT_c) in the nickelate superconductor La3_{3}Ni2_{2}O7_{7}. Using the hopping integrals and on-site potentials obtained by fitting the DFT band structures, we map a quantum phase diagram of a bilayer two-orbital Hubbard model with increasing pressure in a ladder geometry, which has an intermediate Hubbard repulsion and a Hund's coupling. Near 3/83/8 filling, we find a strong spin density wave order, which at 3/83/8 filling shows a real-space spin pattern similar to the spin-charge stripe order along a lattice direction. At 21/6421/64 filling, we find a superconducting phase with interlayer superconductivity (SC) in both the dz2d_{z^2} and dx2y2d_{x^2-y^2} orbitals, as well as in-plane SC in the dz2d_{z^2} orbital. Intriguingly, the SC is weakened with increasing pressure and transits to a Luttinger liquid above 8080 GPa, which qualitatively agrees with the experimental observations of decreasing TcT_c with increasing pressure and a transition to Fermi liquid above 8080 GPa in La3_{3}Ni2_{2}O7_{7}. Through a comparative study, we further show that the ratio of interaction to hopping integral, which reduces moderately with increasing pressure, may play a dominant role in the weakening of SC. Our results of this experimentally relevant model not only find a robust SC through suppressing the competing spin density wave order, but also give new insight into the unusual pressure dependence of SC in La3_{3}Ni2_{2}O7_{7}.

Improved contraction of finite projected entangled pair states

Authors: Markus Scheb

arXiv ID: 2511.01039 | Date: 2025-11-02

Abstract: We present an improved version of the algorithm contracting and optimizing finite projected entangled pair states (fPEPS) in conjunction with projected entangled pair operators (PEPOs). Our work has two components to it. First, we explain in detail the characteristic contraction patterns that occur in fPEPS calculations and how to slice them such that peak memory occupation remains minimal while ensuring efficient parallel computation. Second, we combine controlled bond expansion [A. Gleis, J.-W. Li, and J. von Delft, Phys. Rev. Lett. 130, 246402 (2023)] with randomized singular value decomposition [V. Rokhlin, A. Szlam, and M. Tygert, SIAM J. Matrix Anal. Appl. (2009)] and apply it throughout the fPEPS algorithm. We present benchmark results for the Hubbard model for system sizes up to 8x8 and SU(2) symmetric bond dimension of up to D = 6 for PEPS bonds and χχ = 500 for the environment bonds. Finally, we comment on the state and future of the fPEPS-PEPO framework.

Quantum dynamics in lattices in presence of bulk dephasing and a localized source

Authors: Tamoghna Ray, Katha Ganguly, Dario Poletti, Manas Kulkarni, Bijay Kumar Agarwalla

arXiv ID: 2511.00577 | Date: 2025-11-01

Abstract: The aim of this work is to study the dynamics of quantum systems subjected to a localized fermionic source in the presence of bulk dephasing. We consider two classes of one-dimensional lattice systems: (i) a non-interacting lattice with nearest-neighbor and beyond, i.e., long-ranged (power-law) hopping, and (ii) a lattice that is interacting via short-range interactions modeled by a fermionic quartic Hamiltonian. We study the evolution of the local density profile ni(t)n_i(t) within the system and the growth of the total particle number N(t)N(t) in it. For case (i), we provide analytical insights into the dynamics of the nearest-neighbor model using an adiabatic approximation, which relies on assuming faster relaxation of coherences of the single particle density matrix. For case (ii), we perform numerical computations using the time-evolving block decimation (TEBD) algorithm and analyze the density profile and the growth exponent in N(t)N(t). Our detailed study reveals an interesting interplay between Hamiltonian dynamics and various environmentally induced mechanisms in open quantum systems, such as local source and bulk dephasing. It brings out rich dynamics, including universal dynamical scaling and anomalous behavior across various time scales and is of relevance to various quantum simulation platforms.

Hadronic scattering in (1+1)D SU(2) lattice gauge theory from tensor networks

Authors: João Barata, Juan Hormaza, Zhong-Bo Kang, Wenyang Qian

arXiv ID: 2511.00154 | Date: 2025-10-31

Abstract: We present a first real-time study of hadronic scattering in a (1+1)-dimensional SU(2) lattice gauge theory with fundamental fermions using tensor-network techniques. Working in the gaugeless Hamiltonian formulation -- where the gauge field is exactly integrated out and no truncation of the electric flux is required -- we investigate scattering processes across sectors of fixed global baryon number B=0,1,2B = 0, 1, 2. These correspond respectively to meson-meson, meson-baryon, and baryon-baryon collisions. At strong coupling, the B=0B = 0 and B=2B = 2 channels exhibit predominantly elastic dynamics closely resembling those of the U(1) Schwinger model. In contrast, the mixed B=1B = 1 sector shows qualitatively new behavior: meson and baryon wave packets become entangled during the collision, and depending on their initial kinematics, the slower state becomes spatially delocalized while the faster one propagates ballistically. We characterize these processes through local observables, entanglement entropy, and the information-lattice, which together reveal how correlations build up and relax during the interaction. Our results establish a first benchmark for non-Abelian real-time scattering from first principles and open the path toward quantum-simulation studies of baryon-number dynamics and inelastic processes in gauge theories.

Quantum Hall correlations in tilted extended Bose-Hubbard chains

Authors: Hrushikesh Sable, Subrata Das, Vito W. Scarola

arXiv ID: 2510.27685 | Date: 2025-10-31

Abstract: We demonstrate characteristics of a bosonic fractional quantum Hall (FQH) state in a one-dimensional extended Bose-Hubbard model (eBHM) with a static tilt. In the large tilt limit, quenched kinetic energy leads to emergent dipole moment conservation, enabling mapping to a model generating FQH states. Using exact diagonalization, density matrix renormalization group, and an analytical transfer matrix approach, we analyze energy and entanglement properties to reveal FQH correlations. Our findings set the stage for the use of quenched kinetics in simple time-reversal invariant eBHMs to explore emergent phenomena.

A Comprehensive Stress Test of Truncated Hilbert Space Bases against Green's function Monte Carlo in U(1) Lattice Gauge Theory

Authors: Timo Jakobs, Marco Garofalo, Tobias Hartung, Karl Jansen, Paul Ludwig, Johann Ostmeyer, Simone Romiti, Carsten Urbach

arXiv ID: 2510.27611 | Date: 2025-10-31

Abstract: A representation of Lattice Gauge Theories (LGT) suitable for simulations with tensor network state methods or with quantum computers requires a truncation of the Hilbert space to a finite dimensional approximation. In particular for U(1) LGTs, several such truncation schemes are known, which we compare with each other using tensor network states. We show that a functional basis obtained from single plaquette Hamiltonians -- which we call plaquette state basis -- outperforms the other schemes in two spatial dimensions for plaquette, ground state energy and mass gap, as it is delivering accurate results for a wide range of coupling strengths with a minimal number of basis states. We also show that this functional basis can be efficiently used in three spatial dimensions. Green's function Monte Carlo appears to be a highly useful tool to verify tensor network states results, which deserves further investigation in the future.

Boundary Integrability from the Fuzzy Three Sphere

Authors: Tamas Gombor, Adolfo Holguin

arXiv ID: 2510.27463 | Date: 2025-10-31

Abstract: We consider so4\mathfrak{so}_4 invariant matrix product states (MPS) in the so6\mathfrak{so}_6 symmetric integrable spin chain and prove their integrability. These MPS appear as fuzzy three-sphere solutions of matrix models with Yang-Mills-type interactions, and in particular they correspond to scalar defect sectors of N=4N=4 SYM. We find that the algebra formed by the fuzzy three-sphere generators naturally leads to a boundary reflection algebra and hence a solution to the boundary Yang-Baxter equation for every representation of the fuzzy three-sphere. This allows us to find closed formula for the overlaps of Bethe states of so6\mathfrak{so}_6 symmetric chains with the fuzzy three-sphere MPS for arbitrary bond dimensions.

Engineering Biquadratic Interactions in Spin-1 Chains by Spin-1/2 Spacers

Authors: Yasser Saleem, Weronika Pasek, Marek Korkusinski, Moritz Cygorek, Pawel Potasz

arXiv ID: 2510.26956 | Date: 2025-10-30

Abstract: Low-dimensional quantum systems host a variety of exotic states, such as symmetry-protected topological ground states in spin-1 Haldane chains. Real-world realizations of such states could serve as practical quantum simulators for quantum phases if the interactions can be controlled. However, many proposed models, such as the AKLT state, require unconventional forms of spin interactions beyond standard Heisenberg terms, which do not naturally emerge from microscopic (Coulomb) interactions. Here, we demonstrate a general strategy to induce a biquadratic term between two spin-1 sites and to tune its strength ββ by placing pairs of spin-1/2 spacers in between them. ββ is controlled by the ratio between Heisenberg couplings to and in between the spacer spins. Increasing this ratio increases the magnitude of ββ and decreases the correlation length of edge states, but at a critical value of the ratio, we observe a quantum phase transition between two spin-liquid phases with hidden antiferromagnetic order. Detailed atomistic calculations reveal that chains of nanographene flakes with 22 and 13 atoms, respectively, which could be realized by state-of-the-art bottom-up growth technology, yield precisely the couplings required to approach the AKLT state. These findings deliver a blueprint for engineering unconventional interactions in bottom-up synthesized quantum simulators.

Spin Polarons in Flat Band Ferromagnets

Authors: Saranesh Prembabu, Rahul Sahay, Stefan Divic, Ashvin Vishwanath

arXiv ID: 2510.26798 | Date: 2025-10-30

Abstract: Spin polarons are bound states of electrons and spin-flips that form above spin polarized electronic insulators.These bound states conventionally form in one of two settings: in frustrated lattices with dispersive bands -- where the motion of an electron preferences binding a nearby spin-flip -- or in topological flat bands -- where the Chern number enforces an effective dipolar interaction between electrons and spin flips. In this work, we report the formation of a spin polaron in a context that doesn't fall cleanly into either of these paradigms. In particular, we study the one-dimensional Mielke-Tasaki chain, a paradigmatic model of flat band ferromagnetism, which has an exact ferromagnetic ground state, trivial band topology, and quenched kinetic energy in its lowest band. Despite these features, our density matrix renormalization group simulations reveal the presence of spin polarons upon electron doping this model. More surprisingly, combining these numerics with analytic calculations, we show that polaron binding occurs when the interaction-induced kinetic energy of the model is zero -- contrary to intuition from kinetic magnetism -- and the glue binding the electrons and spin-flips arises from weak mixing with the model's dispersive band -- contrary to what occurs in topological flat bands. Our results open the doors to exploring how the quantum geometry of flat bands drives the formation of exotic charge carriers.

Perfect Particle Transmission through Duality Defects

Authors: Atsushi Ueda, Vic Vander Linden, Laurens Lootens, Jutho Haegeman, Paul Fendley, Frank Verstraete

arXiv ID: 2510.26780 | Date: 2025-10-30

Abstract: We study wavepackets that propagate across (a) topological interfaces in quantum spin systems exhibiting non-invertible symmetries and (b) duality defects coupling dual theories. We demonstrate that the transmission is always perfect, and that a particle traversing the interface is converted into a nonlocal string-like excitation. We give a systematic way of constructing such a defect by identifying its Hilbert space with the virtual bond dimension of the matrix product operator representing defect lines. Our work both gives an operational meaning to topological interfaces, and provides a lattice analogue of recent results solving the monopole paradox in quantum field theory.

Digitized Counterdiabatic Quantum Sampling

Authors: Narendra N. Hegade, Nachiket L. Kortikar, Balaganchi A. Bhargava, Juan F. R. Hernández, Alejandro Gomez Cadavid, Pranav Chandarana, Sebastián V. Romero, Shubham Kumar, Anton Simen, Anne-Maria Visuri, Enrique Solano, Paolo A. Erdman

arXiv ID: 2510.26735 | Date: 2025-10-30

Abstract: We propose digitized counterdiabatic quantum sampling (DCQS), a hybrid quantum-classical algorithm for efficient sampling from energy-based models, such as low-temperature Boltzmann distributions. The method utilizes counterdiabatic protocols, which suppress non-adiabatic transitions, with an iterative bias-field procedure that progressively steers the sampling toward low-energy regions. We observe that the samples obtained at each iteration correspond to approximate Boltzmann distributions at effective temperatures. By aggregating these samples and applying classical reweighting, the method reconstructs the Boltzmann distribution at a desired temperature. We define a scalable performance metric, based on the Kullback-Leibler divergence and the total variation distance, to quantify convergence toward the exact Boltzmann distribution. DCQS is validated on one-dimensional Ising models with random couplings up to 124 qubits, where exact results are available through transfer-matrix methods. We then apply it to a higher-order spin-glass Hamiltonian with 156 qubits executed on IBM quantum processors. We show that classical sampling algorithms, including Metropolis-Hastings and the state-of-the-art low-temperature technique parallel tempering, require up to three orders of magnitude more samples to match the quality of DCQS, corresponding to an approximately 2x runtime advantage. Boltzmann sampling underlies applications ranging from statistical physics to machine learning, yet classical algorithms exhibit exponentially slow convergence at low temperatures. Our results thus demonstrate a robust route toward scalable and efficient Boltzmann sampling on current quantum processors.

Probing Topological Phases in a Strongly Correlated Ladder Model via Entanglement

Authors: Aminul Hussain, Nisa Ara, Rudranil Basu, Sudeshna Sen

arXiv ID: 2510.26713 | Date: 2025-10-30

Abstract: The interplay between non-trivial band topology and strong electronic correlations is a central challenge in modern condensed matter physics. We investigate this competition on a two-leg ladder model with a p-wave-like hybridisation between the legs. This model hosts a symmetry-protected topological phase in its non-interacting limit. Using the density-matrix renormalisation group algorithm, we compute the comprehensive quantum phase diagram in the presence of a repulsive inter-leg density-density interaction. Our analysis, based on entanglement entropy and the entanglement spectrum, reveals a fascinating dichotomy in the stability of the topological phase. We find a non-trivial change in the value of the edge entanglement entropy as we include interaction. Furthermore, we find that the phase boundary separating a trivial insulator phase and a topological one with winding number two remains robustly pinned at its non-interacting location, irrespective of the interaction strength. Variation of the effective conformal field theory's central charge near the critical line explains the robustness of the gap. In contrast, the transition to an insulating phase with winding number one is heavily renormalised, with the critical line shifting significantly as the interaction increases. By successfully mapping the phase diagram and identifying the distinct behaviours of the phase boundaries, our work clarifies how interactions can selectively preserve or destroy different aspects of a topological phase.

Interpretable Artificial Intelligence (AI) Analysis of Strongly Correlated Electrons

Authors: Changkai Zhang, Jan von Delft

arXiv ID: 2510.26864 | Date: 2025-10-30

Abstract: Artificial Intelligence (AI) has become an exceptionally powerful tool for analyzing scientific data. In particular, attention-based architectures have demonstrated a remarkable capability to capture complex correlations and to furnish interpretable insights into latent, otherwise inconspicuous patterns. This progress motivates the application of AI techniques to the analysis of strongly correlated electrons, which remain notoriously challenging to study using conventional theoretical approaches. Here, we propose novel AI workflows for analyzing snapshot datasets from tensor-network simulations of the two-dimensional (2D) Hubbard model over a broad range of temperature and doping. The 2D Hubbard model is an archetypal strongly correlated system, hosting diverse intriguing phenomena including Mott insulators, anomalous metals, and high-TcT_c superconductivity. Our AI techniques yield fresh perspectives on the intricate quantum correlations underpinning these phenomena and facilitate universal omnimetry for ultracold-atom simulations of the corresponding strongly correlated systems.

Phases of Quasi-One-Dimensional Fractional Quantum (Anomalous) Hall - Superconductor Heterostructures

Authors: Steffen Bollmann, Andreas Haller, Jukka I. Väyrynen, Thomas L. Schmidt, Elio J. König

arXiv ID: 2510.26686 | Date: 2025-10-30

Abstract: Motivated by recent observations of fractional Chern insulators (FCIs) in the vicinity of superconducting (SC) phases, we study fractional quantum (anomalous) Hall-superconductor heterostructures in the presence of U(1)U(1) order-parameter fluctuations and particularly focus on the case of ν=2/3ν= 2/3 quantum Hall states leading to Z3\mathbb Z_3 parafermions. We first employ a phenomenological field theory to qualitatively determine the phase diagram. Furthermore, we generalize a previously established alternating pattern of superconductor and tunneling regions, coupled to fractional quantum Hall edge states, to map the problem onto a topological Josephson junction chain involving lattice parafermions. Using density matrix renormalization group simulations, we establish a phase diagram composed of Mott insulating phases and two different Luttinger liquids whose fundamental excitations carry charges 2e and 2e/32e/3, respectively. In agreement with analytical considerations using conformal field theory, we numerically find transitions of Berezinskii-Kosterlitz-Thouless (BKT) type as well as a continuous Z3×U(1)\mathbb Z_3 \times U(1) second-order phase transition characterized by central charge c = 9/5. We finally extract information about a possible ground state degeneracy and comment on the stability of parafermionic edge states in the presence of fluctuations. These theoretical foundations can be expected to be of practical importance for gate-defined FCI-SC heterostructures in moiré materials, in which broad superconducting transitions indicative of strong order parameter fluctuations were observed.

Fractional Chern insulators on cylinders: Tao-Thouless states and beyond

Authors: Felix A. Palm, Chloé Van Bastelaere, Laurens Vanderstraeten

arXiv ID: 2510.26671 | Date: 2025-10-30

Abstract: Topological phases in two-dimensional quantum lattice models are often studied on cylinders for revealing different topological properties and making the problem numerically tractable. This makes a proper understanding of finite-circumference effects crucial for reliably extrapolating the results to the thermodynamic limit. Using matrix product states, we investigate these effects for the Laughlin-1/2 phase in the Hofstadter-Bose-Hubbard model, which can be viewed as the lattice discretization of the bosonic quantum Hall problem in the continuum. We propose a scaling of the model's parameters with the cylinder circumference that simultaneously approaches the continuum and thermodynamic limits. We find that different scaling schemes yield distinct topological signatures: we either retrieve a spontaneous formation of charge density wave ordering reminiscent of the Tao-Thouless states, known from the continuum problem on thin cylinders, or we find uniform states with a topological degeneracy that can be identified as minimally entangled states known from studies of chiral spin liquids on cylinders. Finally, we carry out a similar analysis of the non-Abelian Moore-Read phase in the same model. Our results clarify the role of symmetries in numerical studies of topologically ordered states on cylinders and highlight the role of lattice effects.

A Non-Variational Quantum Approach to the Job Shop Scheduling Problem

Authors: Miguel Angel Lopez-Ruiz, Emily L. Tucker, Emma M. Arnold, Evgeny Epifanovsky, Ananth Kaushik, Martin Roetteler

arXiv ID: 2510.26859 | Date: 2025-10-30

Abstract: Quantum heuristics offer a potential advantage for combinatorial optimization but are constrained by near-term hardware limitations. We introduce Iterative-QAOA, a variant of QAOA designed to mitigate these constraints. The algorithm combines a non-variational, shallow-depth circuit approach using fixed-parameter schedules with an iterative warm-starting process. We benchmark the algorithm on Just-in-Time Job Shop Scheduling Problem (JIT-JSSP) instances on IonQ Forte Generation QPUs, representing some of the largest such problems ever executed on quantum hardware. We compare the performance of the algorithm against both the Variational Quantum Imaginary Time Evolution (VarQITE) algorithm and the non-variational Linear Ramp (LR) QAOA algorithm. We find that Iterative-QAOA robustly converges to find optimal solutions as well as high-quality, near-optimal solutions for all problem instances evaluated. We evaluate the algorithm on larger problem instances up to 97 qubits using tensor network simulations. The scaling behavior of the algorithm indicates potential for solving industrial-scale problems on fault-tolerant quantum computers.

A Non-Variational Quantum Approach to the Job Shop Scheduling Problem

Authors: Miguel Angel Lopez-Ruiz, Emily L. Tucker, Emma M. Arnold, Evgeny Epifanovsky, Ananth Kaushik, Martin Roetteler

arXiv ID: 2510.26859 | Date: 2025-10-30

Abstract: Quantum heuristics offer a potential advantage for combinatorial optimization but are constrained by near-term hardware limitations. We introduce Iterative-QAOA, a variant of QAOA designed to mitigate these constraints. The algorithm combines a non-variational, shallow-depth circuit approach using fixed-parameter schedules with an iterative warm-starting process. We benchmark the algorithm on Just-in-Time Job Shop Scheduling Problem (JIT-JSSP) instances on IonQ Forte Generation QPUs, representing some of the largest such problems ever executed on quantum hardware. We compare the performance of the algorithm against both the Variational Quantum Imaginary Time Evolution (VarQITE) algorithm and the non-variational Linear Ramp (LR) QAOA algorithm. We find that Iterative-QAOA robustly converges to find optimal solutions as well as high-quality, near-optimal solutions for all problem instances evaluated. We evaluate the algorithm on larger problem instances up to 97 qubits using tensor network simulations. The scaling behavior of the algorithm indicates potential for solving industrial-scale problems on fault-tolerant quantum computers.

The Structure of Relation Decoding Linear Operators in Large Language Models

Authors: Miranda Anna Christ, Adrián Csiszárik, Gergely Becsó, Dániel Varga

arXiv ID: 2510.26543 | Date: 2025-10-30

Abstract: This paper investigates the structure of linear operators introduced in Hernandez et al. [2023] that decode specific relational facts in transformer language models. We extend their single-relation findings to a collection of relations and systematically chart their organization. We show that such collections of relation decoders can be highly compressed by simple order-3 tensor networks without significant loss in decoding accuracy. To explain this surprising redundancy, we develop a cross-evaluation protocol, in which we apply each linear decoder operator to the subjects of every other relation. Our results reveal that these linear maps do not encode distinct relations, but extract recurring, coarse-grained semantic properties (e.g., country of capital city and country of food are both in the country-of-X property). This property-centric structure clarifies both the operators' compressibility and highlights why they generalize only to new relations that are semantically close. Our findings thus interpret linear relational decoding in transformer language models as primarily property-based, rather than relation-specific.

Feynman path sum approach for simulation of linear optics

Authors: Wagner F. Balthazar, Quinn M. B. Palmer, Alex. E. Jones, Jake F. F. Bulmer, Ernesto. F. Galvão

arXiv ID: 2510.26408 | Date: 2025-10-30

Abstract: The Feynman path integral formalism has inspired the development of memory-efficient and parallelizable classical algorithms for simulating quantum computers. We adapt this approach for the calculation of probability amplitudes of linear-optical boson sampling experiments, which involve Fock-state inputs, linear optical circuits, and photo-detection at the output. We describe this simulation method and compare it with alternative approaches. Additionally, we implement a Linear-Optical Feynman Path simulator in open-source C code, enhancing its performance using tensor contraction techniques. Our method is benchmarked for low-depth linear optical circuits, where it offers advantages in runtime and memory efficiency.

Programmable digital quantum simulation of 2D Fermi-Hubbard dynamics using 72 superconducting qubits

Authors: Faisal Alam, Jan Lukas Bosse, Ieva Čepaitė, Adrian Chapman, Laura Clinton, Marcos Crichigno, Elizabeth Crosson, Toby Cubitt, Charles Derby, Oliver Dowinton, Paul K. Faehrmann, Steve Flammia, Brian Flynn, Filippo Maria Gambetta, Raúl García-Patrón, Max Hunter-Gordon, Glenn Jones, Abhishek Khedkar, Joel Klassen, Michael Kreshchuk, Edward Harry McMullan, Lana Mineh, Ashley Montanaro, Caterina Mora, John J. L. Morton, Dhrumil Patel, Pete Rolph, Raul A. Santos, James R. Seddon, Evan Sheridan, Wilfrid Somogyi, Marika Svensson, Niam Vaishnav, Sabrina Yue Wang, Gethin Wright

arXiv ID: 2510.26845 | Date: 2025-10-30

Abstract: Simulating the time-dynamics of quantum many-body systems was the original use of quantum computers proposed by Feynman, motivated by the critical role of quantum interactions between electrons in the properties of materials and molecules. Accurately simulating such systems remains one of the most promising applications of general-purpose digital quantum computers, in which all the parameters of the model can be programmed and any desired physical quantity output. However, performing such simulations on today's quantum computers at a scale beyond the reach of classical methods requires advances in the efficiency of simulation algorithms and error mitigation techniques. Here we demonstrate programmable digital quantum simulation of the dynamics of the 2D Fermi-Hubbard model -- one of the best-known simplified models of electrons in crystalline solids -- at a scale beyond exact classical state-vector simulation. We implement simulations of this model on lattice sizes up to 6×6{6\times 6} using 72 qubits on Google's Willow quantum processor, across a range of physical parameters, including different on-site electron-electron interaction strengths and magnetic flux values, and study phenomena including formation of magnetic polarons (charge carriers surrounded by local magnetic polarisation), dynamical symmetry-breaking in stripe-ordered states, attraction of charge carriers on an entangled background state known as a valence bond solid, and the approach to equilibrium through thermalisation. We validate our results against exact calculations in parameter regimes where these are feasible, and compare them to approximate classical simulations performed using tensor network and operator propagation methods. Our results demonstrate that meaningful programmable digital quantum simulation of many-body interacting electron models is now feasible on state-of-the-art quantum hardware.

Fermionic dynamics on a trapped-ion quantum computer beyond exact classical simulation

Authors: Faisal Alam, Jan Lukas Bosse, Ieva Čepaitė, Adrian Chapman, Laura Clinton, Marcos Crichigno, Elizabeth Crosson, Toby Cubitt, Charles Derby, Oliver Dowinton, Norhan Eassa, Paul K. Faehrmann, Steve Flammia, Brian Flynn, Filippo Maria Gambetta, Raúl García-Patrón, Max Hunter-Gordon, Glenn Jones, Abhishek Khedkar, Joel Klassen, Michael Kreshchuk, Edward Harry McMullan, Lana Mineh, Ashley Montanaro, Caterina Mora, John J. L. Morton, Alberto Nocera, Dhrumil Patel, Pete Rolph, Raul A. Santos, James R. Seddon, Evan Sheridan, Wilfrid Somogyi, Marika Svensson, Niam Vaishnav, Sabrina Yue Wang, Gethin Wright, Eli Chertkov, Henrik Dreyer, Michael Foss-Feig

arXiv ID: 2510.26300 | Date: 2025-10-30

Abstract: Simulation of the time-dynamics of fermionic many-body systems has long been predicted to be one of the key applications of quantum computers. Such simulations -- for which classical methods are often inaccurate -- are critical to advancing our knowledge and understanding of quantum chemistry and materials, underpinning a wide range of fields, from biochemistry to clean-energy technologies and chemical synthesis. However, the performance of all previous digital quantum simulations of fermions has been matched by classical methods, and it has thus far remained unclear whether near-term, intermediate-scale quantum hardware could offer any computational advantage in this area. Here, we implement an efficient quantum simulation algorithm on Quantinuum's System Model H2 trapped-ion quantum computer for the time dynamics of a 56-qubit system that is too complex for exact classical simulation. We focus on the periodic spinful 2D Fermi-Hubbard model and present evidence of spin-charge separation, where the elementary electron's charge and spin decouple. In the limited cases where ground truth is available through exact classical simulation, we find that it agrees with the results we obtain from the quantum device. Employing long-range Wilson operators to study deconfinement of the effective gauge field between spinons and the effective potential between charge carriers, we find behaviour that differs from predictions made by classical tensor network methods. Our results herald the use of quantum computing for simulating strongly correlated electronic systems beyond the capacity of classical computing.

Phases and phase transtions in one-dimensional alternating mixed spin (1/2-1) chain: effects of frustration and anisotropy

Authors: Soumya Satpathi, Suparna Sarkar, Swapan K. Pati

arXiv ID: 2510.26223 | Date: 2025-10-30

Abstract: We investigate the phases and phase-transitions in one-dimensional alternating mixed-spin (1/2-1) chain in the presence of both frustration and anisotropy. Frustration is introduced via next-nearest-neighbor interactions, while single-ion anisotropy is incorporated at each lattice site. Our results show that moderate frustration can drive a phase transition from a ferrimagnetic state to an anti-ferromagnetic ground state. Remarkably, the presence of a weak easy-plane anisotropy destabilizes the ferrimagnetic order, also leading to the emergence of an antiferromagnetic phase. Interestingly, under strong frustration and anisotropy, the system exhibits signatures of a novel phase with spin density wave (SDW)-like modulation . We explore these anomalous phase transitions by employing exact diagonalization (ED) for small system sizes and the density matrix renormalization group (DMRG) method to characterize ground state properties for larger system sizes. We also investigate the finite-temperature behavior across various phases using the ancilla-based time-evolving block decimation (TEBD) approach. The primary objective of this work is to elucidate the phase structure of alternating mixed-spin chains under the combined effects of frustration and anisotropy. The primary objective of this work is to elucidate the intricate interplay between frustration and anisotropy in identifying the exotic phases and phase-transitions in alternating mixed-spin chains. Our findings contribute to a deeper understanding of mixed-spin quantum systems and may offer insights for future theoretical and experimental studies.

Heuristic Quantum Advantage with Peaked Circuits

Authors: Hrant Gharibyan, Mohammed Zuhair Mullath, Nicholas E. Sherman, Vincent P. Su, Hayk Tepanyan, Yuxuan Zhang

arXiv ID: 2510.25838 | Date: 2025-10-29

Abstract: We design and demonstrate heuristic quantum advantage with peaked circuits (HQAP circuits) on Quantinuum's System Model H2 quantum processor. Through extensive experimentation with state-of-the-art classical simulation strategies, we identify a clear gap between classical and quantum runtimes. Our largest instance involves all-to-all connectivity with 2000 two-qubit gates, which H2 can produce the target peaked bitstring directly in under 2 hours. Our extrapolations from leading classical simulation techniques such as tensor networks with belief propagation and Pauli path simulators indicate the same instance would take years on exascale systems (Frontier, Summit), suggesting a potentially exponential separation. This work marks an important milestone toward verifiable quantum advantage, as well as providing a useful benchmarking protocol for current utility-scale quantum hardware. We sketch our protocol for designing these circuits and provide extensive numerical results leading to our extrapolation estimates. Separate from our constructed HQAP circuits, we prove hardness on a decision problem involving generic peaked circuits. When both the input and output bitstrings of a peaked circuit are unknown, determining whether the circuit is peaked constitutes a QCMA-complete problem, meaning the problem remains hard even for a quantum polynomial-time machine under commonly accepted complexity assumptions. Inspired by this observation, we propose an application of the peaked circuits as a potentially quantum-safe encryption scheme~\cite{chen2016report,kumar2020post,joseph2022transitioning,dam2023survey}. We make our peaked circuits publicly available and invite the community to try additional methods to solve these circuits to see if this gap persists even with novel classical techniques.

Entanglement-enhanced correlation propagation in the one-dimensional SU(NN) Fermi-Hubbard model

Authors: Mathias Mikkelsen, Ippei Danshita

arXiv ID: 2510.25358 | Date: 2025-10-29

Abstract: We investigate the dynamics of correlation propagation in the one-dimensional Fermi-Hubbard model with SU(NN) symmetry when the replusive-interaction strength is quenched from a large value, at which the ground state is a Mott-insulator with 1/N1/N filling, to an intermediate value. From approximate analytical insights based on a simple model that captures the essential physics of the doublon excitations, we show that entanglement in the initial state leads to collective enhancement of the propagation velocity vSU(N)v_{\text{SU}(N)} when N>2N>2, becoming equal to the velocity of the Bose-Hubbard model in the large-NN limit. These results are supported by numerical calculations of the density-density correlation in the quench dynamics for N=2,3,4,N=2,3,4, and 66.

Finite-Temperature Study of the Hubbard Model via Enhanced Exponential Tensor Renormalization Group

Authors: Changkai Zhang, Jan von Delft

arXiv ID: 2510.25022 | Date: 2025-10-28

Abstract: The two-dimensional (2D) Hubbard model has long attracted interest for its rich phase diagram and its relevance to high-TcT_c superconductivity. However, reliable finite-temperature studies remain challenging due to the exponential complexity of many-body interactions. Here, we introduce an enhanced 1s+1\text{s}^+ eXponential Tensor Renormalization Group algorithm that enables efficient finite-temperature simulations of the 2D Hubbard model. By exploring an expanded space, our approach achieves two-site update accuracy at the computational cost of a one-site update, and delivers up to 50% acceleration for Hubbard-like systems, which enables simulations down to T ⁣ ⁣0.004tT\!\approx\!0.004t. This advance permits a direct investigation of superconducting order over a wide temperature range and facilitates a comparison with zero-temperature infinite Projected Entangled Pair State simulations. Finally, we compile a comprehensive dataset of snapshots spanning the relevant region of the phase diagram, providing a valuable reference for Artificial Intelligence-driven analyses of the Hubbard model and a comparison with cold-atom experiments.

Distinct Types of Parent Hamiltonians for Quantum States: Insights from the WW State as a Quantum Many-Body Scar

Authors: Lei Gioia, Sanjay Moudgalya, Olexei I. Motrunich

arXiv ID: 2510.24713 | Date: 2025-10-28

Abstract: The construction of parent Hamiltonians that possess a given state as their ground state is a well-studied problem. In this work, we generalize this notion by considering simple quantum states and examining the local Hamiltonians that have these states as exact eigenstates. These states often correspond to Quantum Many-Body Scars (QMBS) of their respective parent Hamiltonians. Motivated by earlier works on Hamiltonians with QMBS, in this work we formalize the differences between three distinct types of parent Hamiltonians, which differ in their decompositions into strictly local terms with the same eigenstates. We illustrate this classification using the WW state as the primary example, for which we rigorously derive the complete set of local parent Hamiltonians, which also allows us to establish general results such as the existence of asymptotic QMBS, and distinct dynamical signatures associated with the different parent Hamiltonian types. Finally, we derive more general results on the parent Hamiltonian types that allow us to obtain some immediate results for simple quantum states such as product states, where only a single type exists, and for short-range-entangled states, for which we identify constraints on the admissible types. Altogether, our work opens the door to classifying the rich structures and dynamical properties of parent Hamiltonians that arise from the interplay between locality and QMBS.

Renormalization-group-based preparation of matrix product states on up to 80 qubits

Authors: Moritz Scheer, Alberto Baiardi, Elisa Bäumer Marty, Zhi-Yuan Wei, Daniel Malz

arXiv ID: 2510.24681 | Date: 2025-10-28

Abstract: A key challenge for quantum computers is the efficient preparation of many-body entangled states across many qubits. In this work, we demonstrate the preparation of matrix product states (MPS) using a renormalization-group(RG)-based quantum algorithm on superconducting quantum hardware. Compared to sequential generation, it has been shown that the RG-based protocol asymptotically prepares short-range correlated MPS with an exponentially shallower circuit depth (when scaling system size), but it is not yet clear for which system sizes it starts to convey an advantage. We thus apply this algorithm to prepare a class of MPS exhibiting a phase transition between a symmetry-protected topological (SPT) and a trivial phase for systems of up to 80 qubits. We find that the reduced depth of the RG-based circuits makes them more resilient to noise, and that they generally outperform the sequential circuits for large systems, as we showcase by measuring string-order-like local expectation values and energy densities. We thus demonstrate that the RG-based protocol enables large-scale preparation of MPS and, in particular, SPT-ordered states beyond the fixed point.

Signatures of superconducting pairing driven by electron-electron interactions in moiré WSe2_2/WSe2_2 homobilayer modelled by Hubbard Hamiltonian

Authors: Andrzej Biborski, Michał Zegrodnik

arXiv ID: 2510.24270 | Date: 2025-10-28

Abstract: Strong evidence of unconventional superconductivity has been very recently reported experimentally in twisted transition metal dichalcogenide bilayer and gathered a significant amount of interest. Here we consider the Hubbard model on a triangular lattice describing the hole-doped moiré superlattice emerging in WSe2_{2}/WSe2_{2} twisted homobilayer in the moderately correlated regime. By applying the Density Matrix Renormalization Group, we diagonalize the spin-valley-polarized Hamiltonian and show signatures of coexisting singlet and triplet pairings in the range of hole dopings and displacement fields reported in the experiments. In this view, we show that the superconductivity in the WSe2_{2}/WSe2_{2} twisted homobilayer is likely to be induced by electronic correlations and has a mixed-symmetry character. These predictions can shed light on the nature of the superconducting state observed in the twisted homobilayer of WSe2_{2}/WSe2_{2}. We also identify the emerging superconducting orders, which are dxy(dx2y2±idxy)d_{xy}(d_{x^2-y^2} \pm id_{xy} ) and py(pxipy)p_y(p_{x}\mp ip_{y}) for the singlet and triplet channels in the cylinder of width three(four), respectively.

Pilot-Wave Simulator: Exact Classical Sampling from Ideal and Noisy Quantum Circuits up to Hundreds of Qubits

Authors: Gleb Kalachev, Pavel Mosharev, Zuoheng Zou, Pavel Panteleev, Man-Hong Yung

arXiv ID: 2510.24218 | Date: 2025-10-28

Abstract: Quantum circuit simulators running on classical computers offer a vital platform for designing, testing, and optimizing quantum algorithms, driving innovation despite limited access to real quantum hardware. However, their scalability is inherently constrained by exponential memory and computational overhead, which restricts accurate simulation of large-scale quantum circuits and often results in approximate output distributions. Here, we propose an exact sampling algorithm that integrates tensor network contraction techniques with a Markov process, wherein a classical state evolves according to the local structure of the quantum circuit. As a demonstration, we target the challenge of generating samples from ideal and noisy QAOA circuits with up to 476 qubits, incorporating both depolarizing and amplitude damping noise models. These results enable further validation of several assumptions and conjectures at a scale previously out of reach, significantly expanding the scope of classical simulation in quantum algorithm research.

Matrix product state approach to lossy boson sampling and noisy IQP sampling

Authors: Sojeong Park, Changhun Oh

arXiv ID: 2510.24137 | Date: 2025-10-28

Abstract: Sampling problems have emerged as a central avenue for demonstrating quantum advantage on noisy intermediate-scale quantum devices. However, physical noise can fundamentally alter their computational complexity, often making them classically tractable. Motivated by the recent success of matrix product state (MPS)-based classical simulation of Gaussian boson sampling (Oh et al., 2024), we extend this framework to investigate the classical simulability of other noisy quantum sampling models. We develop MPS-based classical algorithms for lossy boson sampling and noisy instantaneous quantum polynomial-time (IQP) sampling, both of which retain the tunable accuracy characteristic of the MPS approach through the bond dimension. Our approach constructs pure-state decompositions of noisy or lossy input states whose components remain weakly entangled after circuit evolution, thereby providing a means to systematically explore the boundary between quantum-hard and classically-simulable regimes. For boson sampling, we analyze single-photon, Fock, and cat-state inputs, showing that classical simulability emerges at transmission rates scaling as O(1/N)O(1/\sqrt{N}), reaching the known boundary of quantum advantage with a tunable and scalable method. Beyond reproducing previous thresholds, our algorithm offers significantly improved control over the accuracy-efficiency trade-off. It further extends the applicability of MPS-based simulation to broader classes of noisy quantum sampling models, including IQP circuits.

Thermal nature of confining strings

Authors: Sebastian Grieninger, Dmitri E. Kharzeev, Eliana Marroquin

arXiv ID: 2510.23919 | Date: 2025-10-27

Abstract: We investigate the quantum statistical properties of the confining string connecting a static fermion-antifermion pair in the massive Schwinger model. By analyzing the reduced density matrix of the subsystem located in between the fermion and antifermion, we demonstrate that as the interfermion separation approaches the string-breaking distance, the overlap between the microscopic density matrix and an effective thermal density matrix exhibits a pronounced, narrow peak, approaching unity at the onset of string breaking. This behavior reveals that the confining flux tube evolves toward a genuinely thermal state as the separation between the charges grows, even in the absence of an external heat bath. In other words, one cannot tell whether a reduced state of the subsystem arises from a surrounding heat bath or from entanglement with the rest of the system. The entanglement spectrum near the critical string-breaking distance exhibits a rapid transition from the dominance of a single state describing the confining electric string towards a strongly entangled state containing virtual fermion-antifermion pairs. Our findings establish a quantitative link between confinement, entanglement, and emergent thermality, and suggest that string breaking corresponds to a microscopic thermalization transition within the flux tube.

Chiral gapped states are universally non-topological

Authors: Xiang Li, Ting-Chun Lin, Yahya Alavirad, John McGreevy

arXiv ID: 2510.23720 | Date: 2025-10-27

Abstract: We propose an operator generalization of the Li-Haldane conjecture regarding the entanglement Hamiltonian of a disk in a 2+1D chiral gapped groundstate. The logic applies to regions with sharp corners, from which we derive several universal properties regarding corner entanglement. These universal properties follow from a set of locally-checkable conditions on the wavefunction. We also define a quantity (ctot)min(\mathfrak{c}_{\text{tot}})_{\text{min}} that reflects the robustness of corner entanglement contributions, and show that it provides an obstruction to a gapped boundary. One reward from our analysis is that we can construct a local gapped Hamiltonian within the same chiral gapped phase from a given wavefunction; we conjecture that it is closer to the low-energy renormalization group fixed point than the original parent Hamiltonian. Our analysis of corner entanglement reveals the emergence of a universal conformal geometry encoded in the entanglement structure of bulk regions of chiral gapped states that is not visible in topological field theory.

Prediction of a topological phase transition in exchange alternating spin-1 nanographene chains

Authors: João C. G. Henriques, Yelko del Castillo, Ricardo Segundo, Jan Phillips, Joaquín Fernández-Rossier

arXiv ID: 2510.23555 | Date: 2025-10-27

Abstract: The use of magnetic nanographenes as building blocks for artificial spin lattices is enabling the exploration of flagship model Hamiltonians of one-dimensional quantum magnetism with an unprecedented degree of control. The spin-1 Heisenberg model, incorporating both linear and quadratic exchange interactions, was first realized using [3]-triangulenes, where the hallmark Haldane phase with spin fractionalization was observed. Later, the spin-1/2 Heisenberg Hamiltonian with exchange alternation was realized with Clar's goblets, where two additional topological phases were identified. Here we show that spin-1 nanographenes can also be used to explore the topological phase transition between the Haldane phase and a dimerized phase predicted for spin-1 chains with bond-alternation. We first study how the boundary of the phase transition is modified by non-linear exchange, known to be present in spin-1 nanographenes, using density matrix renormalization group (DMRG). Combining multiconfigurational with first-principles calculations, we propose two candidates to realize different topological phases of the model: a recently synthesized extended Clar's goblet, and a passivated [4]-triangulene. Moreover, we show how these two phases can be identified experimentally using inelastic electron tunneling spectroscopy (IETS). This work paves the way for the experimental realization of these topological phases, which can be locally probed with scanning tunneling microscopy.

Variational Thermal State Preparation on Digital Quantum Processors Assisted by Matrix Product States

Authors: Rui-Hao Li, Semeon Valgushev, Khadijeh Najafi

arXiv ID: 2510.23546 | Date: 2025-10-27

Abstract: The preparation of quantum Gibbs states at finite temperatures is a cornerstone of quantum computation, enabling applications in quantum simulation of many-body systems, machine learning via quantum Boltzmann machines, and optimization through thermal sampling techniques. In this work, we introduce a variational framework that leverages matrix product states for the efficient classical evaluation of the Helmholtz free energy, combining scalable entanglement entropy computation with a hardware efficient ansatz to accurately approximate thermal states in one- and two-dimensional systems. We conduct extensive benchmarking on key observables, including energy density, susceptibility, specific heat, and two-point correlations, comparing against exact analytical results for 1D systems and quantum Monte Carlo simulations for 2D lattices across various temperatures and ansatz configurations. Our large-scale numerical simulations demonstrate the capability to prepare high-quality Gibbs states for 1D lattice models with up to 30 sites and 2D systems with up to 6x6 sites, using up to 42 qubits. Finally, we demonstrate the framework's practical viability on a 156-qubit IBM Heron processor by preparing the approximate Gibbs state of a 30-site transverse-field Ising model. Leveraging a combination of error mitigation techniques, we reduce the relative errors in energy and susceptibility measurements by over 50% compared to unmitigated results.

Quantum fluctuations determine the spin-flop transition in hematite

Authors: Tobias Dannegger, Imre Hagymási, Levente Rózsa, Ulrich Nowak

arXiv ID: 2510.23412 | Date: 2025-10-27

Abstract: Magnetic phase transitions between ordered phases are often understood on the basis of semi-classical spin models. Deviations from the classical description due to the quantum nature of the atomic spins as well as quantum fluctuations are usually treated as negligible if long-range order is preserved, and are rarely quantified for actual materials. Here, we demonstrate that a fully quantum-mechanical framework is required for a quantitatively correct description of the spin-flop transition in the insulating altermagnet hematite between the collinear antiferromagnetic and the weakly ferromagnetic spin-flop phase at low temperature. By applying both exact diagonalization and density-matrix renormalization group theory to the quantum Heisenberg Hamiltonian, we show how a quantum-mechanical treatment of an ab initio parametrized spin model can significantly improve the predicted low-temperature spin-flop field over a classical description when compared to measurements. Our results imply that quantum fluctuations have a measurable influence on selecting the ground state of a system out of competing ordered magnetic phases at low temperature.

Ground-state phase diagram of S = 1/2 Heisenberg model on 2D square-hexagon-octagon lattice

Authors: Yumeng Luo, Yuehong Li, Mengfan Jiang, Muwei Wu, Jian-Jian Yang, Dao-Xin Yao, Han-Qing Wu

arXiv ID: 2510.23376 | Date: 2025-10-27

Abstract: Using stochastic series expansion quantum Monte Carlo method and density matrix renormalization group, we study the ground-state phase diagram of S=1/2S=1/2 Heisenberg model on 2D square-hexagon-octagon (SHO) lattice. In this model, we consider two kinds of nearest-neighbor interaction (intra-hexagon interaction J1J_1 and inter-hexagon J2J_2) and the selected third nearest-neighbor interaction J3J_3 along xx direction. From our calculations, there are five phases in the parameters regime 0<λ1=J2/J1<4,0<λ2=J3/J1<40<λ_1=J_2/J_1<4, 0<λ_2=J_3/J_1<4, including a Néel antiferromagentic phase, a Haldane-like symmetry protected topological phase, a hexagon phase and two dimer phases. In the Haldane-like SPT phase, we characterized its topological nature using the degeneracy of ground-state energy under open boundary condition and the entanglement spectrum. To characterize the phase boundaries, we use spin stiffness and Binder cumulant to do the comprehensive finite-size scalings. From data collapse, the critical behaviors of all the nonmagnetic phases to the antiferromagnetic phase belong to the 3D O(3)O(3) Heisenberg universality class. As a theoretical exploration, our work establishes a foundational framework for understanding 2D magnetism on the SHO lattice.

Universal Relations in Long-range Quantum Spin Chains

Authors: Ning Sun, Lei Feng, Pengfei Zhang

arXiv ID: 2510.23135 | Date: 2025-10-27

Abstract: Understanding the emergence of novel collective behaviors in strongly interacting systems lies at the heart of quantum many-body physics. Valuable insight comes from examining how few-body correlations manifest in many-body systems, embodying the ``from few to many'' philosophy. An intriguing example is the set of universal relations in ultracold atomic gases, which connect a wide range of observables to a single quantity known as the contact. In this Letter, we demonstrate that universal relations manifest in a distinct class of quantum many-body systems, long-range quantum spin chains, which belong to a completely new universality class. Using effective field theory and the operator product expansion, we establish connections between the asymptotic behavior of equal-time spin correlation functions, the dynamical structure factor, and the contact density. The theoretical predictions for equal-time correlators are explicitly verified through numerical simulations based on matrix product states. Our results could be readily tested in state-of-the-art trapped-ion systems.

Tensor network methods for quantum-inspired image processing and classical optics

Authors: Nicolas Allegra

arXiv ID: 2510.23089 | Date: 2025-10-27

Abstract: Tensor network methods strike a middle ground between fully-fledged quantum computing and classical computing, as they take inspiration from quantum systems to significantly speed up certain classical operations. Their strength lies in their compressive power and the wide variety of efficient algorithms that operate within this compressed space. In this work, we focus on applying these methods to fundamental problems in image processing and classical optics such as wave-front propagation and optical image formation, by using directly or indirectly parallels with quantum mechanics and computation. These quantum-inspired methods are expected to yield faster algorithms with applications ranging from astronomy and earth observation to microscopy and classical imaging more broadly.

Pinched geometries in 2\mathbf{2}D Lorentzian quantum Regge calculus

Authors: Yoshiyasu Ito, Daisuke Kadoh, Yuki Sato

arXiv ID: 2510.22596 | Date: 2025-10-26

Abstract: We investigate pinched geometries in a two-dimensional Lorentzian model of quantum Regge calculus (QRC) using the tensor renormalization group (TRG) method. A pinched geometry refers to a configuration with an infinitely long temporal extent, even when the total spacetime area is fixed. We examine several choices of integration measures and triangulations to study whether such geometries can dominate in the limit of infinitely many triangles. Our results indicate that pinched geometries are strongly suppressed, and this suppression is observed across different integral measures and triangulations. These results suggest the possible emergence of smooth geometries as well as a sort of universality for infinitely many triangles.

Accelerated Tensor Completion via Trace-Regularized Fully-Connected Tensor Network

Authors: Wenchao Xie, Qingsong Wang, Chengcheng Yan, Zheng Peng

arXiv ID: 2510.22506 | Date: 2025-10-26

Abstract: The fully-connected tensor network (FCTN) decomposition has gained prominence in the field of tensor completion owing to its powerful capacity to capture the low-rank characteristics of tensors. Nevertheless, the recovery of local details in the reconstructed tensor still leaves scope for enhancement. In this paper, we propose efficient tensor completion model that incorporates trace regularization within the FCTN decomposition framework. The trace regularization is constructed based on the mode-kk unfolding of the FCTN factors combined with periodically modified negative laplacian. The trace regularization promotes the smoothness of the FCTN factors through discrete second-order derivative penalties, thereby enhancing the continuity and local recovery performance of the reconstructed tensor. To solve the proposed model, we develop an efficient algorithm within the proximal alternating minimization (PAM) framework and theoretically prove its convergence. To reduce the runtime of the proposed algorithm, we design an intermediate tensor reuse mechanism that can decrease runtime by 10\%-30\% without affecting image recovery, with more significant improvements for larger-scale data. A comprehensive complexity analysis reveals that the mechanism attains a reduced computational complexity. Numerical experiments demonstrate that the proposed method outperforms existing approaches.

Pauli Propagation: Simulating Quantum Spin Dynamics via Operator Complexity

Authors: Yuguo Shao, Song Cheng, Zhengwei Liu

arXiv ID: 2510.22311 | Date: 2025-10-25

Abstract: Simulating real-time quantum dynamics in interacting spin systems is a fundamental challenge, where exact diagonalization suffers from exponential Hilbert-space growth and tensor-network methods face entanglement barriers. In this work, we introduce a scalable Pauli propagation approach that evolves local observables directly in the Heisenberg picture. Theoretically, we derive a priori error bounds governed by the Operator Stabilizer Rényi entropy (OSE) Sα(O)\mathcal{S}^α(O), which explicitly links the truncation accuracy to operator complexity and prescribes a suitable Top-KK truncation strategy. For the 1D Heisenberg model with Jz=0J_z = 0, we prove the number of non-zero Pauli coefficients scales quadratically in Trotter steps, establishing the compressibility of Heisenberg-evolved operators. Numerically, we validate the framework on XXZ Heisenberg chain benchmarks, showing high accuracy with small KK in free regimes (Jz=0J_z = 0) and competitive performance against tensor-network methods (e.g., TDVP) in interacting cases (Jz=0.5J_z = 0.5). These results establish an observable-centric simulator whose cost is governed by operator complexity rather than entanglement, offering a practical alternative for studying non-equilibrium dynamics in quantum many-body systems.

Tractable Shapley Values and Interactions via Tensor Networks

Authors: Farzaneh Heidari, Chao Li, Guillaume Rabusseau

arXiv ID: 2510.22138 | Date: 2025-10-25

Abstract: We show how to replace the O(2^n) coalition enumeration over n features behind Shapley values and Shapley-style interaction indices with a few-evaluation scheme on a tensor-network (TN) surrogate: TN-SHAP. The key idea is to represent a predictor's local behavior as a factorized multilinear map, so that coalitional quantities become linear probes of a coefficient tensor. TN-SHAP replaces exhaustive coalition sweeps with just a small number of targeted evaluations to extract order-k Shapley interactions. In particular, both order-1 (single-feature) and order-2 (pairwise) computations have cost O(n*poly(chi) + n^2), where chi is the TN's maximal cut rank. We provide theoretical guarantees on the approximation error and tractability of TN-SHAP. On UCI datasets, our method matches enumeration on the fitted surrogate while reducing evaluation by orders of magnitude and achieves 25-1000x wall-clock speedups over KernelSHAP-IQ at comparable accuracy, while amortizing training across local cohorts.

Temporal Complexity Hierarchies in Solvable Quantum Many-Body Dynamics

Authors: He-Ran Wang, Ilya Vilkoviskiy, Dmitry A. Abanin

arXiv ID: 2510.21927 | Date: 2025-10-24

Abstract: The influence matrix (IM) provides a powerful framework for characterizing nonequilibrium quantum many-body dynamics by encoding multitime correlations into tensor-network states. Understanding how its computational complexity relates to underlying dynamics is crucial for both theoretical insight and practical utility, yet remains largely unexplored despite a few case studies. Here, we address this question for a family of brickwork quantum circuits ranging from integrable to chaotic regimes. Using tools from geometric group theory, we identify three qualitatively distinct scalings of temporal entanglement entropy, establishing a hierarchy of computational resources required for accurate tensor-network representations of the IM for these models. We further analyze the memory structure of the IM and distinguish between classical and quantum temporal correlations. In particular, for certain examples, we identify effectively classical IMs that admit an efficient Monte Carlo algorithm for computing multitime correlations. In more generic settings without an explicit classical description of the IM, we introduce an operational measure of quantum memory with an experimental protocol, and discuss examples exhibiting long-time genuinely quantum correlations. Our results establish a new connection between quantum many-body dynamics and group theory, providing fresh insights into the complexity of the IM and its intricate connection to the physical characteristics of the dynamics.

SHAP Meets Tensor Networks: Provably Tractable Explanations with Parallelism

Authors: Reda Marzouk, Shahaf Bassan, Guy Katz

arXiv ID: 2510.21599 | Date: 2025-10-24

Abstract: Although Shapley additive explanations (SHAP) can be computed in polynomial time for simple models like decision trees, they unfortunately become NP-hard to compute for more expressive black-box models like neural networks - where generating explanations is often most critical. In this work, we analyze the problem of computing SHAP explanations for *Tensor Networks (TNs)*, a broader and more expressive class of models than those for which current exact SHAP algorithms are known to hold, and which is widely used for neural network abstraction and compression. First, we introduce a general framework for computing provably exact SHAP explanations for general TNs with arbitrary structures. Interestingly, we show that, when TNs are restricted to a *Tensor Train (TT)* structure, SHAP computation can be performed in *poly-logarithmic* time using *parallel* computation. Thanks to the expressiveness power of TTs, this complexity result can be generalized to many other popular ML models such as decision trees, tree ensembles, linear models, and linear RNNs, therefore tightening previously reported complexity results for these families of models. Finally, by leveraging reductions of binarized neural networks to Tensor Network representations, we demonstrate that SHAP computation can become *efficiently tractable* when the network's *width* is fixed, while it remains computationally hard even with constant *depth*. This highlights an important insight: for this class of models, width - rather than depth - emerges as the primary computational bottleneck in SHAP computation.

Tensor Renormalization-Group study of the surface critical behavior of a frustrated two-layer Ising model

Authors: Christophe Chatelain

arXiv ID: 2510.21269 | Date: 2025-10-24

Abstract: Two replicas of a 2D Ising model are coupled by frustrated spin-spin interactions. It is known that this inter-layer coupling is marginal and that the bulk critical behavior belongs to the Ashkin-Teller (AT) universality class, as the J1J_1-J2J_2 Ising model. In this work, the surface critical behavior is studied numerically by Tensor Renormalization-Group calculations. The Bond-Weight Tensor Renormalization Group algorithm is extended to tackle systems with boundaries. It is observed that the two-fold degeneracy of the surface magnetic scaling dimension of the AT model is lifted in the frustrated two-layer Ising model (F2LIM). The splitting is explained by the breaking of the Z2{\mathbb Z}_2-symmetry under spin reversal of a single Ising replica in the F2LIM. The two distinct surface magnetic scaling dimensions x1sx_1^s and x2sx_2^s of the F2LIM satisfies a simple duality relation x1s=1/4x2sx_1^s=1/4x_2^s.

Tensor-Network study of Ising model on infinite hyperbolic dodecahedral lattice

Authors: Matej Mosko, Andrej Gendiar

arXiv ID: 2510.20939 | Date: 2025-10-23

Abstract: We propose a tensor-network-based algorithm to study the classical Ising model on an infinitely large hyperbolic lattice with a regular 3D tesselation of identical dodecahedra. We reformulate the corner transfer matrix renormalization group (CTMRG) algorithm from 2D to 3D to reproduce the known results on the cubic lattice. Consequently, we generalize the CTMRG to the hyperbolic dodecahedral lattice, which is an infinite-dimensional lattice. We analyze the spontaneous magnetization, von Neumann entropy, and correlation length to find a continuous non-critical phase transition on the dodecahedral lattice. The phase transition temperature is estimated to be Tpt4.66T_{\rm pt} \approx 4.66. We find the magnetic critical exponents β=0.4999β= 0.4999 and δ=3.007δ=3.007 that confirm the mean-field universality class in accord with predictions of Monte Carlo and high-temperature series expansions. The algorithm can be applied to arbitrary multi-state spin models.

Local-to-Global Entanglement Dynamics by Periodically Driving Impurities

Authors: Zhi-Xing Lin, Abhinav Prem, Shinsei Ryu, Bastien Lapierre

arXiv ID: 2510.20908 | Date: 2025-10-23

Abstract: We study the entanglement dynamics of a one-dimensional spin chain subject to a local Floquet drive of a two-site impurity. We uncover a sharp transition in the entanglement dynamics as a function of the driving frequency. For large drive periods TT, we observe a linear growth in entanglement entropy (EE), indicating a heating phase with volume law entanglement. Surprisingly, for driving periods below a critical value TT_\ast, the EE grows subextensively with time, characteristic of a local quantum quench. In the non-interacting limit, we analytically trace the origin of this phenomenon to a transition in the single-particle Floquet quasi-energy spectrum. We also find that for T>TT>T_*, the so-called ``average energy" operator develops non-local, rainbow-like couplings that are responsible for the rapid entanglement growth in the heating phase, but remains local for T<TT<T_*. Using extensive matrix-product-state simulations, we show that the non-heating phase and the subextensive entanglement growth persist in the presence of weak interactions for numerically accessible timescales. Our results establish that local Floquet engineering can generate emergent bulk phenomena, shedding new light on energy localization and thermalization in driven many-body systems.

Systematic study of multi-magnon binding energies in the FM-AFM J1J_1-J2J_2 chain

Authors: Satoshi Nishimoto

arXiv ID: 2510.20633 | Date: 2025-10-23

Abstract: We present a systematic study of multi-magnon bound states (MBSs) in the spin-12\tfrac{1}{2} FM-AFM J1J_1-J2J_2 chain under magnetic fields using the density-matrix renormalization group method. As a quantitative measure of stability, we compute the magnon binding energy Eb(M,p)E_{\rm b}(M,p) for bound clusters of size pp over wide ranges of the frustration ratio J2/J1J_2/|J_1| and the normalized magnetization M/MsM/M_{\rm s}. Near saturation, we benchmark our data against the analytic two-magnon result and map out a clear hierarchy of pp-magnon states, whose phase boundaries follow an empirical scaling J2,c(p;p ⁣+ ⁣1)/J1 ⁣ ⁣0.34p2.3J_{2,{\rm c}}(p;p\!+\!1)/|J_1|\!\approx\!0.34\,p^{-2.3} for large pp. We further quantify the relation between the most stable pp and the zero-field pitch angle θθ, verifying the conjectured inequality 1/p>θ/π>1/(p+1)1/p>θ/π>1/(p+1) up to p9p \lesssim 9. The binding energy shows pronounced suppression as J2/J1 ⁣ ⁣1/4+J_2/|J_1|\!\to\!1/4^+ and, for some frustration values, attains a maximum below full saturation, indicating that partial depolarization enhances bound-magnon mobility. Close to the FM instability, Eb(Ms,p)E_{\rm b}(M_{\rm s},p) exhibits an empirical power-law vanishing consistent with a quantum-Lifshitz scenario. Our results provide a comprehensive, experimentally relevant map of MBS stability across field and frustration, offering concrete guidance for inelastic probes in quasi-one-dimensional magnets.

Temperley-Lieb categories with coloured regions and Jones-Wenzl projectors

Authors: Cameron Howat, Robert Laugwitz, Martin Ray

arXiv ID: 2510.20613 | Date: 2025-10-23

Abstract: Generalised Temperley-Lieb categories with regions labelled by elements of a commutative algebra were introduced by M. Khovanov and the second author in [Pure Appl. Math. Q. 19 (2023), no. 5]. We consider the case where the regions are labelled by colours, corresponding to a complete set of orthogonal idempotents of a semisimple commutative algebra. We determine when these generalised Temperley-Lieb categories are semisimple and find the direct sum decompositions of tensor products of simple objects. As the main tool we use two-variable versions of Chebychev polynomials and coloured Jones-Wenzl projectors. As a consequence, we prove a conjecture of M. Khovanov and the second author on Gram determinants and non-degeneracy of trace pairings for the associated Temperley-Lieb algebras with coloured regions.

Computing excited states with isometric tensor networks in two-dimensions

Authors: Alec Dektor, Runze Chi, Roel Van Beeumen, Chao Yang

arXiv ID: 2510.20063 | Date: 2025-10-22

Abstract: We present a new subspace iteration method for computing low-lying eigenpairs (excited states) of high-dimensional quantum many-body Hamiltonians with nearest neighbor interactions on two-dimensional lattices. The method is based on a new block isometric projected entangled pair state (block-isoPEPS) ansatz that generalizes the block matrix product state (MPS) framework, widely used for Hamiltonians defined on one-dimensional chains, to two-dimensions. The proposed block-isoPEPS ansatz offers several attractive features for PEPS-based algorithms, including exact block orthogonalization, controlled local truncation via singular value decompositions, and efficient evaluation of observables. We demonstrate the proposed inexact subspace iteration for block-isoPEPS by computing excitations of the two-dimensional transverse-field Ising and Heisenberg models and compare our results with existing PEPS methods. Our results demonstrate that block isometric tensor networks provide a scalable framework for studying excitations in quantum many-body systems beyond one dimension.

Quantum Hall to Chiral Spin Liquid transition in a Triangular Lattice Hofstadter-Hubbard Model

Authors: Cesar A. Gallegos, Rafael M. Magaldi, Andrew Millis, Steven R. White

arXiv ID: 2510.19907 | Date: 2025-10-22

Abstract: We investigate the weak interaction integer quantum Hall (IQH) phase, the intermediate interaction phase identified as a chiral spin liquid (CSL) and the transition between them in the triangular lattice Hofstadter-Hubbard model at a density of one electron per site in an orbital magnetic field corresponding to one-quarter flux per plaquette. Our primary tool is the finite system density matrix renormalization group (DMRG) method with both interaction-strength scan and fixed interaction techniques for cylinders of circumference 3, 5, and 7 and lengths up to 240. For the IQH phase, we use single particle exact diagonalization to clarify finite size effects, including an excess charge on the edges of our cylinders, and the limitations of entanglement spectra degeneracies on small circumference cylinders. For both phases, we use DMRG to study the entanglement spectra, the entanglement entropy, and the effect of flux insertion on charge and spin pumping, all of which show key differences between the two phases. To study the transition, we use interaction-strength scans extending between the two phases, and apply a scaling data collapse of a bond-dimerization order parameter to extract critical exponents. We also extract critical behavior from the divergence of correlation lengths on the IQH side, measuring decay away from edges of both the dimerization order parameter and transverse edge currents. The critical behavior and exponents are consistent with an Ising transition in 1+1 dimensions. Finally, we obtain excited states in various quantum number sectors finding that the gap to a charge neutral momentum ππ excitation corresponding to fluctuations of the dimerization order parameter closes in the vicinity of the critical point but gaps to other excitations remain large.

KARIPAP: Quantum-Inspired Tensor Network Compression of Large Language Models Using Infinite Projected Entangled Pair States and Tensor Renormalization Group

Authors: Azree Nazri

arXiv ID: 2510.21844 | Date: 2025-10-22

Abstract: Large Language Models (LLMs) like ChatGPT and LLaMA drive rapid progress in generative AI, yet their huge parameter scales create severe computational and environmental burdens. High training costs, energy use, and limited device deployment hinder accessibility. Existing compression - pruning, distillation, low-rank, and quantization - reduces size but ignores complex inter-layer correlations. We propose KARIPAP, a quantum-inspired tensor network compression using Infinite Projected Entangled Pair States (iPEPS) and Tensor Renormalization Group (TRG) contraction. Unlike 1D Matrix Product States, iPEPS captures multi-directional entanglement in attention and deep transformer layers. TRG ensures polynomial-time contraction, making tensorization feasible while preserving key correlation geometry. Experiments on LLaMA-2 7B show up to 93% memory and 70% parameter reduction, with 50% faster training, 25% faster inference, and only 2-3% accuracy loss. Layer-wise entanglement profiling reveals redundancy in deeper layers, confirming their suitability for tensor factorization. KARIPAP demonstrates that modern LLMs occupy low-dimensional entanglement manifolds, enabling scalable, energy-efficient, and quantum-aware AI architectures.

Discrete Shift and Polarization from Response to Symmetry Defects in Interacting Topological Phases

Authors: Lu Zhang, Min Long, Yuxuan Zhang, Zi Yang Meng, Xue-Yang Song

arXiv ID: 2510.19483 | Date: 2025-10-22

Abstract: We extend the previous study of extracting crystalline symmetry-protected topological invariants to the correlated regime. We construct the interacting Hofstadter model defined on square lattice with the rotation and translation symmetry defects: disclination and dislocation. The model realizes Chern insulator and the charge density wave state as one tunes interactions. Employing the density matrix renormalization group (DMRG) method, we calculate the excess charge around the defects and find that the topological invariants remain quantized in both phases, with the topological quantity extracted to great precision. This study paves the way for utilizing matrix product state, and potentially other quantum many-body computation methods, to efficiently study crystalline symmetry defects on 2D interacting lattice systems.

Lattice-reflection symmetry in tensor-network renormalization group with entanglement filtering in two and three dimensions

Authors: Xinliang Lyu, Naoki Kawashima

arXiv ID: 2510.19428 | Date: 2025-10-22

Abstract: Tensor-network renormalization group (TNRG) is an efficient real-space renormalization group method for studying the criticality in both classical and quantum lattice systems. Exploiting symmetries of a system in a TNRG algorithm can simplify the implementation of the algorithm and can help produce correct tensor RG flows. Although a general framework for considering a global on-site symmetry has been established, it is still unclear how to incorporate a lattice symmetry like rotation or reflection in TNRG. As a first step for lattice symmetries, we propose a method to incorporate the lattice-reflection symmetry in the context of a TNRG with entanglement filtering in both two and three dimensions (2D and 3D). To achieve this, we write down a general definition of lattice-reflection symmetry in tensor-network language. Then, we introduce a transposition trick for exploiting and imposing the lattice-reflection symmetry in two basic TNRG operators: projective truncations and entanglement filtering. Using the transposition trick, the detailed algorithms of the TNRG map in both 2D and 3D are laid out, where the lattice-reflection symmetry is preserved and imposed. Finally, we demonstrate how to construct the linearization of the TNRG maps in a given lattice-reflection sector, with the help of which it becomes possible to extract scaling dimensions in each sector separately. Our work paves the way for understanding the lattice-rotation symmetry in TNRG.

Hybrid Quantum-Classical Eigensolver with Real-Space Sampling and Symmetric Subspace Measurements

Authors: Lei Xu, Ling Wang

arXiv ID: 2510.19219 | Date: 2025-10-22

Abstract: We propose a hybrid quantum-classical eigensolver to address the computational challenges of simulating strongly correlated quantum many-body systems, where the exponential growth of the Hilbert space and extensive entanglement render classical methods intractable. Our approach combines real-space sampling of tensor-network-bridged quantum circuits with symmetric subspace measurements, effectively constraining the wavefunction within a substaintially reduced Hilbert space for efficient and scalable simulations of versatile target states. The system is partitioned into equal-sized subsystems, where quantum circuits capture local entanglement and tensor networks reconnect them to recover global correlations, thereby overcoming partition-induced limitations. Symmetric subspace measurements exploit point-group symmetries through a many-to-one mapping that aggregates equivalent real-space configurations into a single symmetric state, effectively enhancing real-space bipartition entanglement while elimilating redundant degrees of freedom. The tensor network further extends this connectivity across circuits, restoring global entanglement and correlation, while simultaneously enabling generative sampling for efficient optimization. As a proof of concept, we apply the method to the periodic J1 ⁣ ⁣J2J_1\!-\!J_2 antiferromagnetic Heisenberg model in one and two dimensions, incorporating translation, reflection, and inversion symmetries. With a small matrix product state bond dimension of up to 6, the method achieves an absolute energy error of 10510^{-5} for a 64-site periodic chain and a 6×66\times6 torus after bond-dimension extrapolation. These results validate the accuracy and efficiency of the hybrid eigensolver and demonstrate its strong potential for scalable quantum simulations of strongly correlated systems.

Calculating the Luttinger liquid parameter for an interacting Kitaev chain quantum simulator

Authors: Troy Losey, Jin Zhang, S. -W. Tsai

arXiv ID: 2510.19189 | Date: 2025-10-22

Abstract: In this work, we introduce a solid-state platform for building quantum simulators using implanted spin centers in solid-state materials. We build upon the proposal for an S=1S=1 chain of spin centers coupled through the magnetic dipole-dipole interaction and subjected to an external magnetic field as a quantum simulator for critical floating phases. We introduce another magnetic field and map the system to the interacting Kitaev chain. This setup, tunable through the applied fields and the orientation of the spin centers within the crystal, exhibits a variety of rich quantum behavior which notably includes floating phases, a Z2Z_2 symmetry-breaking phase, and lines of both Berezinskii-Kosterlitz-Thouless (BKT) and Pokrovsky-Talapov transitions. Furthermore, we employ several novel methods to calculate the Luttinger liquid parameter in our model with incommensurate correlations. We find that these methods provide a route to identify BKT transitions with less computational resources than utilizing entanglement entropy and central charge.

On the stabilizer complexity of Hawking radiation

Authors: Ritam Basu, Onkar Parrikar, Suprakash Paul, Harshit Rajgadia

arXiv ID: 2510.18967 | Date: 2025-10-21

Abstract: We study the complexity of Hawking radiation for an evaporating black hole from the perspective of the stabilizer theory of quantum computation. Specifically, we calculate Wigner negativity -- a magic monotone which can be interpreted as a measure of the stabilizer complexity, or equivalently, the complexity of classical simulation -- in various toy models for evaporating black holes. We first calculate the Wigner negativity of Hawking radiation in the PSSY model directly using the gravitational path integral, and show that the negativity is O(1)O(1) before the Page transition, but becomes exponentially large past the Page transition. We also derive a universal, information theoretic formula for the negativity which interpolates between the two extremes. We then study the Wigner negativity of radiation in a dynamical model of black hole evaporation. In this case, the negativity shows a sharp spike at early times resulting from the coupling between the black hole and the radiation system, but at late times when the system settles down, we find that the negativity satisfies the same universal formula as in the PSSY model. Finally, we also propose a geometric formula for Wigner negativity in general holographic states using intuition from fixed area states and random tensor networks, and argue that a python's lunch in the entanglement wedge implies a stabilizer complexity which is exponentially large in 18GN\frac{1}{8G_N} times the difference between the areas corresponding to the outermost and minimal extremal surfaces.

Repulsively Bound Hadrons in a Z2\mathbb{Z}_2 Lattice Gauge Theory

Authors: Sayak Guha Roy, Vaibhav Sharma, Kaidi Xu, Umberto Borla, Jad C. Halimeh, Kaden R. A. Hazzard

arXiv ID: 2510.23618 | Date: 2025-10-21

Abstract: A paradigmatic model, the Z2\mathbb{Z}_2 lattice gauge theory exhibits confinement mediated by the gauge field that binds pairs of particles into mesons, drawing connections to quantum chromodynamics. In the absence of any additional attractive interactions between particles, mesons are not known to bind in this model. Here, we show that resonant pair-production terms give rise to an additional repulsive binding mechanism that forms a stable ``hadron'' bound state of two mesons. A high-energy state, the hadron is stabilized by being off-resonantly coupled to a continuum. We study the dynamical formation of this bound state starting from local excitations. We use matrix product state techniques based on the time-evolving block decimation algorithm to perform our numerical simulations and analyze the effect of model parameters on hadron formation. Furthermore, we derive an effective model that explains its formation. Our findings are amenable to experimental observation on modern quantum hardware from superconducting qubits to trapped ions.

Haerter-Shastry kinetic magnetism and metallicity in the triangular Hubbard model

Authors: Sogoud Sherif, Prakash Sharma, Aman Kumar, Hitesh J. Changlani

arXiv ID: 2510.18954 | Date: 2025-10-21

Abstract: The fermionic Hubbard model, when combined with the ingredient of frustration, associated with the breaking of particle-hole symmetry, harbors a rich phase diagram. Aspects of theoretical findings associated with the nature of magnetism and metallicity, in a diverse set of parameter regimes, are now being actively investigated in triangular Hubbard cold atom and solid-state (moiré) based emulators. Building on the theoretical work of Haerter and Shastry [Phys. Rev. Lett. 95,087202 (2005)], we explore the impact of kinetically frustrated magnetism, a phenomenon where antiferromagnetic order emerges without any underlying magnetic interactions, at finite hole density. We numerically study the infinite-UU triangular Hubbard model using the density matrix renormalization group algorithm and estimate the extent of stability of the kinetically induced 120120^{\circ} antiferromagnetic state to hole doping. Beyond the Haerter-Shastry regime, we find an intermediate phase with multimer (involving multiple correlated spins) stripes that eventually gives way to a paramagnet. We also find evidence of gapless charge excitations (metallicity) throughout the phase diagram for finite hole density. We discuss the implications at large, but finite and realistic values of U/tU/t, and investigate whether kinetic magnetism and superexchange collaborate or compete.

Growth and collapse of subsystem complexity under random unitary circuits

Authors: Jeongwan Haah, Douglas Stanford

arXiv ID: 2510.18805 | Date: 2025-10-21

Abstract: For chaotic quantum dynamics modeled by random unitary circuits, we study the complexity of reduced density matrices of subsystems as a function of evolution time where the initial global state is a product pure state. The state complexity is defined as the minimum number of local quantum channels to generate a given state from a product state to a good approximation. In 1+11+1d, we prove that the complexity of subsystems of length \ell smaller than half grows linearly in time TT at least up to T=/4T = \ell / 4 but becomes zero after time T=/2T = \ell /2 in the limit of a large local dimension, while the complexity of the complementary subsystem of length larger than half grows linearly in time up to exponentially late times. Using holographic correspondence, we give some evidence that the state complexity of the smaller subsystem should actually grow linearly up to time T=/2T = \ell/2 and then abruptly decay to zero.

Renormalized dual basis for scalable simulations of 2+1D compact quantum electrodynamics

Authors: Marc Miranda-Riaza, Pierpaolo Fontana, Alessio Celi

arXiv ID: 2510.18594 | Date: 2025-10-21

Abstract: The classical and quantum simulation of lattice gauge theories (LGTs) with Lie groups is hindered by the infinite-dimensional Hilbert space of gauge degrees of freedom. In a recent work [Phys. Rev. X 15, 031065 (2025)], we introduced a new truncation scheme -- here renamed as Renormalized Dual Basis (RDB) -- based on the resolution of the single-plaquette problem, and demonstrated its performance for SU(2) LGTs. In this paper, we apply the RDB to compact quantum electrodynamics (cQED) in three spacetime dimensions (2+1D). We variationally determine the ground state of the theory for small lattices with periodic (for pure gauge) and open (in presence of fermionic matter) boundary conditions, achieving improved precision for the plaquette operator compared to previous approaches. By leveraging tensor networks, we extend the study to larger lattices and demonstrate the scalability of the method. Overall, we show that the RDB provides an efficient description across all coupling regimes.

Fingerprints of cluster-based Haldane and bound-magnon states in a spin-1 Heisenberg diamond chain

Authors: Azam Zoshki, Hamid Arian Zad, Katarina Karlova, Jozef Strecka

arXiv ID: 2510.18447 | Date: 2025-10-21

Abstract: We investigate magnetic and thermodynamic properties of a spin-1 Heisenberg diamond chain in a magnetic field using a combination of analytical and numerical methods including the variational approach, exact diagonalization, density-matrix renormalization group, localized-magnon theory, and quantum Monte Carlo simulations. In the unfrustrated regime, the model exhibits a quantum ferrimagnetic phase that captures key magnetic features of the nickel-based polymeric compound [Ni3(OH)2(C4H2O4)(H2O)4].2H2O such as a at minimum in the temperature dependence of the susceptibility times temperature product and an intermediate one-third magnetization plateau. In the frustrated regime, we uncover a rich variety of unconventional quantum phases including uniform and cluster-based Haldane states, fragmented monomer-dimer phase, and bound-magnon crystals. Analysis of the adiabatic temperature change and magnetic Gruneisen parameter reveals an enhanced magnetocaloric effect near field-induced transitions between these exotic quantum phases. Additionally, we demonstrate that the frustrated spin-1 diamond chain can operate as an efficient working medium of a quantum Stirling engine, which approaches near-optimal efficiency when driven into these unconventional quantum states.

Bayesian Fully-Connected Tensor Network for Hyperspectral-Multispectral Image Fusion

Authors: Linsong Shan, Zecan Yang, Laurence T. Yang, Changlong Li, Honglu Zhao, Xin Nie

arXiv ID: 2510.18400 | Date: 2025-10-21

Abstract: Tensor decomposition is a powerful tool for data analysis and has been extensively employed in the field of hyperspectral-multispectral image fusion (HMF). Existing tensor decomposition-based fusion methods typically rely on disruptive data vectorization/reshaping or impose rigid constraints on the arrangement of factor tensors, hindering the preservation of spatial-spectral structures and the modeling of cross-dimensional correlations. Although recent advances utilizing the Fully-Connected Tensor Network (FCTN) decomposition have partially alleviated these limitations, the process of reorganizing data into higher-order tensors still disrupts the intrinsic spatial-spectral structure. Furthermore, these methods necessitate extensive manual parameter tuning and exhibit limited robustness against noise and spatial degradation. To alleviate these issues, we propose the Bayesian FCTN (BFCTN) method. Within this probabilistic framework, a hierarchical sparse prior that characterizing the sparsity of physical elements, establishes connections between the factor tensors. This framework explicitly models the intrinsic physical coupling among spatial structures, spectral signatures, and local scene homogeneity. For model learning, we develop a parameter estimation method based on Variational Bayesian inference (VB) and the Expectation-Maximization (EM) algorithm, which significantly reduces the need for manual parameter tuning. Extensive experiments demonstrate that BFCTN not only achieves state-of-the-art fusion accuracy and strong robustness but also exhibits practical applicability in complex real-world scenarios.

Entanglement Spectrum Resolved by Loop Symmetries

Authors: Haruki Yagi, Zongping Gong

arXiv ID: 2510.18350 | Date: 2025-10-21

Abstract: A rigorous analysis is presented for the entanglement spectrum of quantum many-body states possessing a higher-form group-representation symmetry generated by topological Wilson loops, which is generally non-invertible. A general framework based on elementary algebraic topology and category theory is developed to determine the block structure of reduced density matrices for arbitrary bipartite manifolds on which the states are defined. Within this framework, we scrutinize the impact of topology on the entanglement structure for low-dimensional manifolds, including especially the torus, the Klein bottle, and lens spaces. By further incorporating gauge invariance, we refine our framework to determine the entanglement structure for topological gauge theories in arbitrary dimensions. In particular, in two dimensions, it is shown for the Kitaev quantum double model that not only the topological entanglement entropy can be reproduced, but also the Li-Haldane conjecture concerning the full entanglement spectrum holds exactly.

Efficient Tensor Completion Algorithms for Highly Oscillatory Operators

Authors: Navjot Singh, Edgar Solomonik, Xiaoye Sherry Li, Yang Liu

arXiv ID: 2510.17734 | Date: 2025-10-20

Abstract: This paper presents low-complexity tensor completion algorithms and their efficient implementation to reconstruct highly oscillatory operators discretized as n×nn\times n matrices. The underlying tensor decomposition is based on the reshaping of the input matrix and its butterfly decomposition into an order O(logn)O (\log n) tensor. The reshaping of the input matrix into a tensor allows for representation of the butterfly decomposition as a tensor decomposition with dense tensors. This leads to efficient utilization of the existing software infrastructure for dense and sparse tensor computations. We propose two tensor completion algorithms in the butterfly format, using alternating least squares and gradient-based optimization, as well as a novel strategy that uses low-rank matrix completion to efficiently generate an initial guess for the proposed algorithms. To demonstrate the efficiency and applicability of our proposed algorithms, we perform three numerical experiments using simulated oscillatory operators in seismic applications. In these experiments, we use O(nlogn)O (n \log n) observed entries in the input matrix and demonstrate an O(nlog3n)O(n\log^3 n) computational cost of the proposed algorithms, leading to a speedup of orders of magnitudes per iteration for large matrices compared to the low-rank matrix and quantized tensor-train completion. Moreover, the proposed butterfly completion algorithms, equipped with the novel initial guess generation strategy, achieve reconstruction errors that are smaller by an order of magnitude, enabling accurate recovery of the underlying structure compared to the state-of-the-art completion algorithms.

Non-stabilizerness as a Diagnostic of Criticality and Exceptional Points in Non-Hermitian Spin Chains

Authors: Cătălin Paşcu Moca, Doru Sticlet, Balázs Dóra

arXiv ID: 2510.17248 | Date: 2025-10-20

Abstract: We investigate non-stabilizerness, also known as ``magic,'' to understand criticality and exceptional points in non-Hermitian quantum many-body systems. Our focus is on parity-time (PT\mathcal{PT}) symmetric spin chains, specifically the non-Hermitian transverse-field Ising and XX models. We calculate stabilizer Rényi entropies in their ground states using non-Hermitian matrix product state methods. Our findings show that magic exhibits unique and model-specific signs of phase transitions. In the Ising chain, it peaks along the regular Hermitian-like critical line but disappears across exceptional points. In contrast, in the XX chain, it reaches its maximum at the exceptional line where PT\mathcal{PT} symmetry is broken. Finite-size scaling reveals that these effects become more pronounced with larger systems, highlighting non-stabilizerness as a sensitive marker for both quantum criticality and non-Hermitian spectral degeneracies. We also investigate magic in momentum space for the XX model analytically and find that is reaches a minimum around exceptional points. Our results indicate that magic takes extremal values at the exceptional points and serves as a valuable tool for examining complexity, criticality, and symmetry breaking in non-Hermitian quantum matter.

Finite-temperature signatures of underlying superconductivity in the electron-doped Hubbard model

Authors: Wen O. Wang, Thomas P. Devereaux

arXiv ID: 2510.16616 | Date: 2025-10-18

Abstract: We perform numerically exact determinant quantum Monte Carlo simulations of the Hubbard model and analyze pairing tendencies by evaluating correlation functions at the imaginary-time midpoint (τ=β/2τ=β/2), which suppresses high-frequency weight and emphasizes low-energy physics. Using this diagnostic, we identify clear finite-temperature signatures of underlying dd-wave superconductivity for electron doping, while finding no clear indication upon cooling for hole doping. Our analysis enables direct comparison with ground-state DMRG, revealing consistent real-space pairing patterns. These results provide a practical route to bridge the gap between finite-temperature and ground-state numerically exact simulations of the Hubbard model despite the fermion sign problem.

High order Tensor-Train-Based Schemes for High-Dimensional Mean Field Games

Authors: Elisabetta Carlini, Luca Saluzzi

arXiv ID: 2510.15603 | Date: 2025-10-17

Abstract: We introduce a fully discrete scheme to solve a class of high-dimensional Mean Field Games systems. Our approach couples semi-Lagrangian (SL) time discretizations with Tensor-Train (TT) decompositions to tame the curse of dimensionality. By reformulating the classical Hamilton-Jacobi-Bellman and Fokker-Planck equations as a sequence of advection-diffusion-reaction subproblems within a smoothed policy iteration, we construct both first and second order in time SL schemes. The TT format and appropriate quadrature rules reduce storage and computational cost from exponential to polynomial in the dimension. Numerical experiments demonstrate that our TT-accelerated SL methods achieve their theoretical convergence rates, exhibit modest growth in memory usage and runtime with dimension, and significantly outperform grid-based SL in accuracy per CPU second.

Adaptive quantum channel discrimination using methods of quantum metrology

Authors: Stanisław Sieniawski, Rafał Demkowicz-Dobrzański

arXiv ID: 2510.15506 | Date: 2025-10-17

Abstract: We present an efficient tensor-network based algorithm for finding the optimal adaptive quantum channel discrimination strategies inspired by recently developed numerical methods in quantum metrology to find the optimal adaptive channel estimation protocols. We examine the connection between channel discrimination and estimation problems, highlighting in particular an appealing structural similarity between models that admit Heisenberg scaling estimation performance, and models that admit perfect channel discrimination in finite--number of channel uses.

Fractional Quantum Hall Wedding Cakes

Authors: Chloé Van Bastelaere, Felix A. Palm, Botao Wang, Nathan Goldman, Laurens Vanderstraeten

arXiv ID: 2510.15472 | Date: 2025-10-17

Abstract: This work investigates the coexistence of distinct topologically ordered phases within a single setup. We demonstrate this concept through tensor network simulations of the Hofstadter-Bose-Hubbard model under a spatially modulated chemical potential. Focusing on cylindrical geometries, we realize regions exhibiting the Laughlin-1/2 phase and its particle-hole conjugate, and confirm their topological character via the local Středa's response and Laughlin's flux insertion protocol. Our approach offers a new pathway for experimentally and numerically charting entire phase diagrams within a single system, possibly eliminating the need for independent parameter scans.

Sequence Modeling with Spectral Mean Flows

Authors: Jinwoo Kim, Max Beier, Petar Bevanda, Nayun Kim, Seunghoon Hong

arXiv ID: 2510.15366 | Date: 2025-10-17

Abstract: A key question in sequence modeling with neural networks is how to represent and learn highly nonlinear and probabilistic state dynamics. Operator theory views such dynamics as linear maps on Hilbert spaces containing mean embedding vectors of distributions, offering an appealing but currently overlooked perspective. We propose a new approach to sequence modeling based on an operator-theoretic view of a hidden Markov model (HMM). Instead of materializing stochastic recurrence, we embed the full sequence distribution as a tensor in the product Hilbert space. A generative process is then defined as maximum mean discrepancy (MMD) gradient flow in the space of sequences. To overcome challenges with large tensors and slow sampling convergence, we introduce spectral mean flows, a novel tractable algorithm integrating two core concepts. First, we propose a new neural architecture by leveraging spectral decomposition of linear operators to derive a scalable tensor network decomposition of sequence mean embeddings. Second, we extend MMD gradient flows to time-dependent Hilbert spaces and connect them to flow matching via the continuity equation, enabling simulation-free learning and faster sampling. We demonstrate competitive results on a range of time-series modeling datasets. Code is available at https://github.com/jw9730/spectral-mean-flow.

Unsupervised Learning to Recognize Quantum Phases of Matter

Authors: Mehran Khosrojerdi, Alessandro Cuccoli, Paola Verrucchi, Leonardo Banchi

arXiv ID: 2510.14742 | Date: 2025-10-16

Abstract: Drawing the quantum phase diagram of a many-body system in the parameter space of its Hamiltonian can be seen as a learning problem, which implies labelling the corresponding ground states according to some classification criterium that defines the phases. In this work we adopt unsupervised learning, where the algorithm has no access to any priorly labeled states, as a tool for determining quantum phase diagrams of many-body systems. The algorithm directly works with quantum states: given the ground-state configurations for different values of the Hamiltonian parameters, the process uncovers the most significant way of grouping them based on a similarity criterion that refers to the fidelity between quantum states, that can be easily estimated, even experimentally. We benchmark our method with two specific spin-12\frac{1}{2} chains, with states determined via tensor network techniques. We find that unsupervised learning algorithms based on spectral clustering, combined with ``silhouette'' and ``elbow'' methods for determining the optimal number of phases, can accurately reproduce the phase diagrams. Our results show how unsupervised learning can autonomously recognize and possibly unveil novel phases of quantum matter.

Bosonic Laughlin and Moore-Read states from non-Chern flat bands

Authors: Hongyu Lu, Wang Yao

arXiv ID: 2510.14685 | Date: 2025-10-16

Abstract: The rapid advances in the study of fractional Chern insulators (FCIs) raise a fundamental question: while initially discovered in flat Chern bands motivated by their topological equivalence to Landau levels, is single- particle band topology actually a prerequisite for these many-body topological orders emergent at fractional fillings? Here, we numerically demonstrate bosonic FCIs in two types of non-Chern flat bands in honeycomb lattices, using exact diagonalization and density matrix renormalization group calculations. In a gapless flat band with a singular band touching, we observe a Laughlin state at half filling, stabilized by onsite interactions from the hard-core limit down to arbitrarily small strength. Furthermore, we report the first example of a non- Abelian FCI in a non-Chern band system: a Moore-Read state at νν = 1 filling of the same singular flat band with hard-core bosons. Under lattice parameters that realize a gapped trivial band (C = 0) of exact flatness, we also find the Laughlin FCI of soft-core bosons in the isolated band limit where onsite interaction is much smaller than the band gap. In this case, the FCI forms as interacting bosons spontaneously avoid the peaks in quantum metric and Berry curvature, preferentially occupying Brillouin zone region with relatively uniform quantum geometry. Our work significantly expands the landscape for (non-)Abelian FCIs and broadens the understanding of their formation beyond the Chern band paradigm.

On the Identifiability of Tensor Ranks via Prior Predictive Matching

Authors: Eliezer da Silva, Arto Klami, Diego Mesquita, Iñigo Urteaga

arXiv ID: 2510.14523 | Date: 2025-10-16

Abstract: Selecting the latent dimensions (ranks) in tensor factorization is a central challenge that often relies on heuristic methods. This paper introduces a rigorous approach to determine rank identifiability in probabilistic tensor models, based on prior predictive moment matching. We transform a set of moment matching conditions into a log-linear system of equations in terms of marginal moments, prior hyperparameters, and ranks; establishing an equivalence between rank identifiability and the solvability of such system. We apply this framework to four foundational tensor-models, demonstrating that the linear structure of the PARAFAC/CP model, the chain structure of the Tensor Train model, and the closed-loop structure of the Tensor Ring model yield solvable systems, making their ranks identifiable. In contrast, we prove that the symmetric topology of the Tucker model leads to an underdetermined system, rendering the ranks unidentifiable by this method. For the identifiable models, we derive explicit closed-form rank estimators based on the moments of observed data only. We empirically validate these estimators and evaluate the robustness of the proposal.

Quantum machine learning and quantum-inspired methods applied to computational fluid dynamics: a short review

Authors: Cesar A. Amaral, Vinícius L. Oliveira, Juan P. L. C. Salazar, Eduardo I. Duzzioni

arXiv ID: 2510.14099 | Date: 2025-10-15

Abstract: Computational Fluid Dynamics (CFD) is central to science and engineering, but faces severe scalability challenges, especially in high-dimensional, multiscale, and turbulent regimes. Traditional numerical methods often become prohibitively expensive under these conditions. Quantum computing and quantum-inspired methods have been investigated as promising alternatives. This review surveys advances at the intersection of quantum computing, quantum algorithms, machine learning, and tensor network techniques for CFD. We discuss the use of Variational Quantum Algorithms as hybrid quantum-classical solvers for PDEs, emphasizing their ability to incorporate nonlinearities through Quantum Nonlinear Processing Units. We further review Quantum Neural Networks and Quantum Physics-Informed Neural Networks, which extend classical machine learning frameworks to quantum hardware and have shown advantages in parameter efficiency and solution accuracy for certain CFD benchmarks. Beyond quantum computing, we examine tensor network methods, originally developed for quantum many-body systems and now adapted to CFD as efficient high-dimensional compression and solver tools. Reported studies include several orders of magnitude reductions in memory and runtime while preserving accuracy. Together, these approaches highlight quantum and quantum-inspired strategies that may enable more efficient CFD solvers. This review closes with perspectives: quantum CFD remains out of reach in the NISQ era, but quantum-inspired tensor networks already show practical benefits, with hybrid approaches offering the most promising near-term strategy.

Temporal Entanglement Transitions in the Periodically Driven Ising Chain

Authors: Karun Gadge, Abhinav Prem, Rishabh Jha

arXiv ID: 2510.13970 | Date: 2025-10-15

Abstract: Periodically driven quantum systems can host non-equilibrium phenomena without static analogs, including in their entanglement dynamics. Here, we discover temporaltemporal entanglemententanglement transitionstransitions in a Floquet spin chain, which correspond to a quantum phase transition in the spectrum of the entanglement Hamiltonian and are signaled by dynamical spontaneous symmetry breaking. We show that these transitions are entanglement-driven, i.e., they require initially entangled states and remain invisible to conventional local observables. Intriguingly, we find these transitions across a broad range of driving frequencies (from adiabatic to high-frequency regime) and independently of drive details, where they manifest as periodic, sharp entanglement spectrum reorganizations marked by the Schmidt-gap closure, a vanishing entanglement echo, and symmetry-quantum-number flips. At high frequencies, the entanglement Hamiltonian acquires an intrinsic timescale decoupled from the drive period, rendering the transitions genuine steady-state features. Finite-size scaling reveals universal critical behavior with correlation-length exponent ν=1ν=1, matching equilibrium Ising universality despite its emergence from purely dynamical mechanisms decoupled from static criticality. Our work establishes temporal entanglement transitions as novel features in Floquet quantum matter.

Diffeomorphism invariant tensor networks for 3d gravity

Authors: Vijay Balasubramanian, Charlie Cummings

arXiv ID: 2510.13941 | Date: 2025-10-15

Abstract: Tensor networks prepare states that share many features of states in quantum gravity. However, standard constructions are not diffeomorphism invariant and do not support an algebra of non-commuting area operators. Recently, analogues of both problems were addressed in a tensor network discretization of topological field theories (TFT) with finite or compact gauge groups. Here, we extend this work towards gravity by generalizing to gauge groups that are discrete or continuous, compact or non-compact. Applied to SL(2,R)×SL(2,R)\text{SL}(2,\mathbb{R}) \times \text{SL}(2,\mathbb{R}) Chern-Simons theory, our construction can be interpreted as building states of three dimensional gravity with a negative cosmological constant. Our tensor networks prepare states that satisfy the constraints of Chern-Simons theory. In metric variables, this implies that the states we construct satisfy the Wheeler-DeWitt equation and momentum constraints, and so are diffeomorphism invariant.

Quantum-inspired space-time PDE solver and dynamic mode decomposition

Authors: Raghavendra Dheeraj Peddinti, Stefano Pisoni, Narsimha Rapaka, Mohamed K. Riahi, Egor Tiunov, Leandro Aolita

arXiv ID: 2510.21767 | Date: 2025-10-15

Abstract: Numerical solutions of partial differential equations (PDEs) are central to the understanding of dynamical systems. Standard approaches involving time-stepping schemes compute the solution at each time step, which becomes too costly when simulating long-term dynamics. Alternatively, space-time methods that treat the combined space-time domain simultaneously promise better stability and accuracy. Interestingly, data-driven approaches for learning and predicting dynamics, such as dynamic mode decomposition (DMD), also employ a combined space-time representation. However, the curse of dimensionality often limits the practical benefits of space-time methods. In this work, we investigate quantum-inspired methods for space-time approaches, both for solving PDEs and for making DMD predictions. We achieve this goal by treating both spatial and temporal dimensions within a single matrix product state (MPS) encoding. First, we benchmark our MPS space-time solver for both linear and nonlinear PDEs, observing that the MPS ansatz accurately captures the underlying spatio-temporal correlations while having significantly fewer degrees of freedom. Second, we develop an MPS-DMD algorithm to make accurate long-term predictions of nonlinear systems, with runtime scaling logarithmically in both spatial and temporal resolution. This research highlights the role of tensor networks in developing effective and interpretable models, bridging the gap between numerical methods and data-driven approaches.

Emergent Discrete Time Crystals on Digital Quantum Computers: Boundary-Protected and Ancilla-Induced Disorder Mechanisms of Thermalization Slowdown

Authors: Kazuya Shinjo, Kazuhiro Seki, Seiji Yunoki

arXiv ID: 2510.13577 | Date: 2025-10-15

Abstract: Periodically driven (Floquet) systems typically evolve toward an infinite-temperature thermal state due to continuous energy absorption. Before reaching equilibrium, however, they can transiently exhibit long-lived prethermal states that host exotic nonequilibrium phenomena, such as discrete time crystals (DTCs). In this study, we investigate the relaxation dynamics of periodically driven product states in a kicked Ising model implemented on the IBM Quantum Eagle and Heron processors. By using ancilla qubits to mediate interactions, we construct Kagome and Lieb lattices on superconducting qubits with heavy-hex connectivity. We identify two distinct types of noise-induced DTCs on Kagome and Lieb lattices, both arising from quantum noise in ancilla qubits. Type-I DTCs originate from robust boundary-mode period-doubling oscillations, stabilized by symmetry charge pumping, that are redistributed into the bulk due to ancilla noise. Type-II DTCs, in contrast, emerge in systems without charge-pumped qubits, where quantum noise unexpectedly stabilizes period-doubling oscillations that would otherwise rapidly decay. On the noisier Eagle device (ibm_kyiv), we observe both type-I and type-II DTCs on 53-qubit Kagome lattices with and without charge-pumped qubits, respectively. In contrast, on the lower-noise Heron device (ibm_marrakesh), period-doubling oscillations are confined to boundary-localized oscillations on 82-qubit Kagome and 40-qubit Lieb lattices, as redistribution into the bulk is suppressed. These experimental findings are supported by noisy matrix-product-state simulations, in which ancilla noise is modeled as random sign flips in the two-qubit gate rotation angles. Our results demonstrate that quantum noise in ancilla qubits can give rise to novel classes of prethermal dynamical phases, including boundary-protected and noise-induced DTCs.

Functional tensor train neural network for solving high-dimensional PDEs

Authors: Yani Feng, Michael K. Ng, Kejun Tang, Zhiwen Zhang

arXiv ID: 2510.13386 | Date: 2025-10-15

Abstract: Discrete tensor train decomposition is widely employed to mitigate the curse of dimensionality in solving high-dimensional PDEs through traditional methods. However, the direct application of the tensor train method typically requires uniform grids of regular domains, which limits its application on non-uniform grids or irregular domains. To address the limitation, we develop a functional tensor train neural network (FTTNN) for solving high-dimensional PDEs, which can represent PDE solutions on non-uniform grids or irregular domains. An essential ingredient of our approach is to represent the PDE solutions by the functional tensor train format whose TT-core functions are approximated by neural networks. To give the functional tensor train representation, we propose and study functional tensor train rank and employ it into a physics-informed loss function for training. Because of tensor train representation, the resulting high-dimensional integral in the loss function can be computed via one-dimensional integrals by Gauss quadrature rules. Numerical examples including high-dimensional PDEs on regular or irregular domains are presented to demonstrate that the performance of the proposed FTTNN is better than that of Physics Informed Neural Networks (PINN).

The Kitaev-AKLT model

Authors: Alwyn Jose Raja, R. Ganesh

arXiv ID: 2510.12880 | Date: 2025-10-14

Abstract: Inspired by the Affleck-Kennedy-Lieb-Tasaki (AKLT) model, we present exact solutions for a spin-1 chain with Kitaev-like couplings. We consider an expanded Kitaev model with bilinear and biquadratic terms. At an exactly solvable point, the Hamiltonian can be reexpressed as a sum of projection operators. Unlike the AKLT model where projectors act on total spin, we project onto components of spin along the bond direction. This leads to exponential ground state degeneracy, expressed in terms of fractionalized spin-12\frac{1}{2} objects. Each ground state can be expressed concisely as a matrix product state. We construct a phase diagram by varying the relative strength of bilinear and biquadratic terms. The fractionalized states provide a qualitative picture for the spin-1 Kitaev model, yielding approximate forms for the ground state and low-lying excitations.

Measurement-induced entanglement in noisy 2D random Clifford circuits

Authors: Zhi-Yuan Wei, Jon Nelson, Joel Rajakumar, Esther Cruz, Alexey V. Gorshkov, Michael J. Gullans, Daniel Malz

arXiv ID: 2510.12743 | Date: 2025-10-14

Abstract: We study measurement-induced entanglement generated by column-by-column sampling of noisy 2D random Clifford circuits of size NN and depth TT. Focusing on the operator entanglement SopS_{\rm op} of the sampling-induced boundary state, first, we reproduce in the noiseless limit a finite-depth transition from area- to volume-law scaling. With on-site probablistic trace noise at any constant rate p>0p>0, the maximal SopS_{\rm op} attained along the sampling trajectory obeys an area law in the boundary length and scales approximately linearly with T/pT/p. By analyzing the spatial distribution of stabilizer generators, we observe exponential localization of stabilizer generators; this both accounts for the scaling of the maximal SopS_{\rm op} and implies an exponential decay of conditional mutual information across buffered tripartitions, which we also confirm numerically. Together, these results indicate that constant local noise destroys long-range, volume-law measurement-induced entanglement in 2D random Clifford circuits. Finally, based on the observed scaling, we conjecture that a tensor-network-based algorithm can efficiently sample from noisy 2D random Clifford circuits (i) at sub-logarithmic depths T=o(logN)T = o(\log N) for any constant noise rate p=Ω(1)p = Ω(1), and (ii) at constant depths T=O(1)T = O(1) for noise rates p=Ω(log1N)p = Ω(\log^{-1}N).

The anisotropic Heisenberg model close to the Ising limit: triangular lattice vs. effective models

Authors: Martin Ulaga, Jure Kokalj, Takami Tohyama, Peter Prelovšek

arXiv ID: 2510.12667 | Date: 2025-10-14

Abstract: Stimulated by recent experiments on materials representing the realization of the anisotropic Heisenberg spin-1/21/2 model on the triangular lattice, we explore further properties of such a model in the easy-axis regime α=J/Jz<1α= J_\perp/J_z < 1, as well as effective models that also capture such physics. We show that anisotropic Heisenberg models on the honeycomb lattice and even on the square lattice reveal similarities to the full triangular lattice in the magnetization curve as well as in the transverse magnetization (superfluid) order parameter mm_\perp at finite fields. Still, at α1α\ll 1, results reveal gapless excitations and small but finite m>0m_\perp >0 at effective fields corresponding to the triangular case without the field. In contrast, several additional numerical studies of the full model on the triangular lattice confirm the existence of the gap at α1α\ll 1. In particular, the magnetization curve m(h)m(h) as well as the spin stiffness ρsρ_s indicate (at zero field) a transition/crossover from gapped to gapless regime at ααα\sim α^* with α0.5α^* \lesssim 0.5. We also show that deviations from the linear spin-wave theory and the emergence of the gap can be traced back to the strong effective repulsion between magnon excitations, having similarity to strongly correlated systems.

Quantum Spin Singlet and Classical Néel-Ordered Ground States in MoX3 (X = I, Br) Spin-3/2 Dimerized Antiferromagnetic Chain Crystals

Authors: Jordan Teeter, Topojit Debnath, Harshil Goyal, Md Sabbir Hossen Bijoy, Maedeh Taheri, Nicholas Sesing, Fariborz Kargar, Kirill Shtengel, Tina Salguero, Roger K. Lake, Alexander A. Balandin

arXiv ID: 2510.12613 | Date: 2025-10-14

Abstract: We report that MoX3 (X = I, Br) are rare van der Waals materials that exhibit signatures of both quantum spin chains with a spin singlet ground state and classical Neel order. Bulk single crystals grown by chemical vapor transport exhibit classical antiferromagnetic ground states with a transition temperature of ~40 K as revealed by susceptibility and specific heat measurements. Above 40 K, the susceptibilities show the large, broad peaks associated with a quantum spin-singlet ground state and large singlet-triplet gaps of 21 meV and 25 meV. Monte Carlo simulations, density matrix renormalization-group calculations for finite spin-3/2 chains, and density functional theory reproduce the experimental behavior, confirming the interplay between strong one-dimensional intrachain and weak three-dimensional interchain couplings. MoX3 offers a unique platform for exploring quantum magnetism and magnetic excitations at the atomic chain limit, as these materials combine a 1D van der Waals motif, spin chain behavior, and classical interchain order.

Bound on entanglement in neural quantum states

Authors: Nisarga Paul

arXiv ID: 2510.11797 | Date: 2025-10-13

Abstract: Variational wavefunctions offer a practical route around the exponential complexity of many-body Hilbert spaces, but their expressive power is often sharply constrained. Matrix product states, for instance, are efficient but limited to area law entangled states. Neural quantum states (NQS) are widely believed to overcome such limitations, yet little is known about their fundamental constraints. Here we prove that feed-forward neural quantum states acting on nn spins with kk scalar nonlinearities, under certain analyticity assumptions, obey a bound on entanglement entropy for any subregion: ScklognS \leq c k\log n, for a constant cc. This establishes an NQS analog of the area law constraint for matrix product states and rules out volume law entanglement for NQS with O(1)O(1) nonlinearities. We demonstrate analytically and numerically that the scaling with nn is tight for a wide variety of NQS. Our work establishes a fundamental constraint on NQS that applies broadly across different network designs, while reinforcing their substantial expressive power.

Qiboml: towards the orchestration of quantum-classical machine learning

Authors: Matteo Robbiati, Andrea Papaluca, Andrea Pasquale, Edoardo Pedicillo, Renato M. S. Farias, Alejandro Sopena, Mattia Robbiano, Ghaith Alramahi, Simone Bordoni, Alessandro Candido, Niccolò Laurora, Jogi Suda Neto, Yuanzheng Paul Tan, Michele Grossi, Stefano Carrazza

arXiv ID: 2510.11773 | Date: 2025-10-13

Abstract: We present Qiboml, an open-source software library for orchestrating quantum and classical components in hybrid machine learning workflows. Building on Qibo's quantum computing capabilities and integrating with popular machine learning frameworks such as TensorFlow and PyTorch, Qiboml enables the construction of quantum and hybrid models that can run on a broad range of backends: (i) multi-threaded CPUs, GPUs, and multi-GPU systems for simulation with statevector or tensor network methods; (ii) quantum processing units, both on-premise and through cloud providers. In this paper, we showcase its functionalities, including diverse simulation options, noise-aware simulations, and real-time error mitigation and calibration.

Efficient and accurate tensor network algorithm for Anderson impurity problems

Authors: Zhijie Sun, Zhenyu Li, Chu Guo

arXiv ID: 2510.11459 | Date: 2025-10-13

Abstract: The Anderson impurity model (AIM) is of fundamental importance in condensed matter physics to study strongly correlated effects. However, accurately solving its long-time dynamics still remains a great numerical challenge. An emergent and rapidly developing numerical strategy to solve the AIM is to represent the Feynman-Vernon influence functional (IF), which encodes all the bath effects on the impurity dynamics, as a matrix product state (MPS) in the temporal domain. The computational cost of this strategy is basically determined by the bond dimension χχ of the temporal MPS. In this work, we propose an efficient and accurate method which, when the hybridization function in the IF can be approximated as the summation of nn exponential functions, can systematically build the IF as a MPS by multiplying O(n)O(n) small MPSs, each with bond dimension 22. Our method gives a worst case scaling of χχ as 28n2^{8n} and 22n2^{2n} for real- and imaginary-time evolution respectively. We demonstrate the performance of our method for two commonly used bath spectral functions, where we show that the actually required χχs are much smaller than the worst case.

Tensor-Network-Based Unraveling of Non-Markovian Dynamics in Large Spin Chains via the Influence Martingale Approach

Authors: Sujay Mondal, Siddhartha Dutta, Abhijit Bandyopadhyay

arXiv ID: 2510.11200 | Date: 2025-10-13

Abstract: Classical simulation of open quantum system dynamics remains challenging due to the exponential growth of the Hilbert space, the need to accurately capture dissipation and decoherence, and the added complexity of memory effects in the non-Markovian regime. We develop an efficient algorithm for simulating both Markovian and non-Markovian dynamics in large one-dimensional quantum systems. Extending the Tensor Jump Method, which combines TDVP-based tensor-network evolution with a Suzuki-Trotter decomposition of stochastic trajectories, our approach incorporates time-dependent decay rates-treating positive rates as time-inhomogeneous Markovian processes and negative rates via the Influence Martingale formalism to unravel time-local non-Markovian dynamics. This resource-efficient framework enables scalable simulations of open-system dynamics in the non-Markovian regime, as demonstrated for a one-dimensional transverse-field Ising chain comprising up to 100 spin qubits.

Features of preparable entangled states in Gaussian quantum networks

Authors: Shuanping Du, Zhaofang Bai

arXiv ID: 2510.10167 | Date: 2025-10-11

Abstract: Large-scale quantum networks have been employed to overcome practical constraints on transmission and storage for single entangled systems. The deterministic preparation of entangled states is one of the key factors for realization of quantum networks. There is no efficient method to verify whether single multipartite entanglement can be prepared by multisource quantum networks. Here, we theoretically analysize under what conditions entangled states can be prepared in three kinds of basic Gaussian quantum networks, named triangle networks, star-shaped networks and chain-type networks. Some necessity criteria are derived for all preparable entangled Gaussian states in such networks. It shows that the network structure imposes strong constraints on the set of preparable entangled Gaussian states, which is fundamentally different with the standard single multipartite entanglement. This takes the first step towards understanding network mechanism for preparing entangled Gaussian states.

Efficient Emulation of Neutral Atom Quantum Hardware

Authors: Kemal Bidzhiev, Stefano Grava, Pablo le Henaff, Mauro Mendizabal, Elie Merhej, Anton Quelle

arXiv ID: 2510.09813 | Date: 2025-10-10

Abstract: Simulating the dynamics of neutral atom arrays is a challenging problem. To address this, we introduce two emulators, emu-sv and emu-mps, as computational backends for Pasqal's pulser package. Emu-sv is designed for high-precision state-vector simulations, giving the possibility to emulate systems of up to 27\thicksim 27 qubits on an A100 40GB GPU, making it perfect for cases where numerically exact results are needed. In contrast, emu-mps uses a Matrix Product State representation and other controlled approximations to efficiently simulate much larger arrays of atoms with manageable errors. We show through benchmark comparisons that both emulators provide significant speed-ups over generic solvers such as QuTiP. In addition, we provide practical guidance on choosing between the two emulators. These quantum software tools are designed to support researchers and developers aiming to simulate quantum systems either as a precursor to full hardware implementation or as a means of benchmarking hardware performance.

Tensor-based compression of the sea temperature data

Authors: Ilya Kosolapov, Tatiana Sheloput, Sergey Matveev

arXiv ID: 2510.09778 | Date: 2025-10-10

Abstract: In this work we investigate efficient data compression for spatiotemporal Black, Azov and Marmara Seas temperature tensors that contain significant number of missing values. These tensors have a complex structure influenced by the coastlines and bathymetry, as well as temporal temperature changes. While such missing data typically provokes utilization of tensor completion algorithms, we demonstrate that standard SVD-based compression approaches (including the Tucker, Tensor-Train (TT) and Quantized-TT formats) are remarkably effective and yield comparable results. We propose a greedy spatial data partitioning algorithm enhancing their performance. We divide the data into the smaller subtensors before compression via exploitation of this trick. Furthermore, our analysis reveals a strong temporal dependency in the data's compressibility caused by its nature. Fixing the level of precision we observe a significant seasonal variation. Investigating this, we find that a temporal partitioning on a scale of approximately two days is nearly optimal for all tested tensor based formats. The combined application of these spatial and temporal strategies with tensor methods ultimately achieves a robust compression ratio of 5 times across the entire dataset.

Conformal Data for the O(3) Wilson-Fisher CFT from Fuzzy Sphere Realization of Quantum Rotor Model

Authors: Arjun Dey, Loic Herviou, Christopher Mudry, Andreas Martin Läuchli

arXiv ID: 2510.09755 | Date: 2025-10-10

Abstract: We present a model for strongly interacting fermions with internal O(3) symmetry on the fuzzy-sphere that (i) preserves the rotational symmetry of the fuzzy sphere and (ii) undergoes a quantum phase transition in the (2+1)-dimensional O(3) Wilson-Fisher universality class. Using exact diagonalization (ED) and density matrix renormalization group (DMRG), we locate the quantum critical point via conformal perturbation theory and obtain scaling dimensions from finite-size spectra. We identify 24 primary operators and determine some of their operator product expansion coefficients through first-order conformal perturbation theory. The results are benchmarked against conformal bootstrap and large quantum-number expansions and reveal a weakly irrelevant operator that plays a role in dimerized antiferromagnets. Our work establishes the fuzzy sphere as a general framework for quantitatively accessing conformal data in non-Abelian conformal field theories (CFTs).

Vari-Cool: a non-unitary quantum variational protocol for simulated cooling

Authors: Jeffrey Z. Song, Gilad Kishony, Erez Berg, Mark S. Rudner

arXiv ID: 2510.09749 | Date: 2025-10-10

Abstract: We introduce a variational approach for preparing low energy states of arbitrary target Hamiltonians. The protocol is defined in terms of a repeated cycle consisting of p layers of unitary gates applied to the system and ancilla "bath" qubits, followed by reset of the bath qubits. The gate parameters within each cycle are optimized such that the steady state achieved after many cycles has a low energy expectation value with respect to the target Hamiltonian, and that the energy converges toward the steady state value in as few cycles as possible. We illustrate the protocol for the transverse field Ising model, and study its systematic behaviors with respect to system size, model parameters, and noise using tensor network based classical simulations. We then experimentally demonstrate its operation on IBM's ibm_kingston quantum processor for up to 28 system qubits coupled to 14 bath sites. Classical training on small system sizes and with few unitary layers per cycle gives robust results that transfer well to larger system sizes and to noisy hardware.

A Quantum-Inspired Algorithm for Solving Sudoku Puzzles and the MaxCut Problem

Authors: Max B. Zhao, Fei Li

arXiv ID: 2510.19835 | Date: 2025-10-10

Abstract: We propose and evaluate a quantum-inspired algorithm for solving Quadratic Unconstrained Binary Optimization (QUBO) problems, which are mathematically equivalent to finding ground states of Ising spin-glass Hamiltonians. The algorithm employs Matrix Product States (MPS) to compactly represent large superpositions of spin configurations and utilizes a discrete driving schedule to guide the MPS toward the ground state. At each step, a driver Hamiltonian -- incorporating a transverse magnetic field -- is combined with the problem Hamiltonian to enable spin flips and facilitate quantum tunneling. The MPS is updated using the standard Density Matrix Renormalization Group (DMRG) method, which iteratively minimizes the system's energy via multiple sweeps across the spin chain. Despite its heuristic nature, the algorithm reliably identifies global minima, not merely near-optimal solutions, across diverse QUBO instances. We first demonstrate its effectiveness on intermediate-level Sudoku puzzles from publicly available sources, involving over 200200 Ising spins with long-range couplings dictated by constraint satisfaction. We then apply the algorithm to MaxCut problems from the Biq Mac library, successfully solving instances with up to 251251 nodes and 3,2653,265 edges. We discuss the advantages of this quantum-inspired approach, including its scalability, generalizability, and suitability for industrial-scale QUBO applications.

Superconductivity in the repulsive Hubbard model on different geometries induced by density-assisted hopping

Authors: Franco T. Lisandrini, Edmond Orignac, Roberta Citro, Ameneh Sheikhan, Corinna Kollath

arXiv ID: 2510.09363 | Date: 2025-10-10

Abstract: We study the effect of density-assisted hopping on different dimerized lattice geometries, such as bilayers and ladder structures. We show analytically that the density-assisted hopping induces an attractive interaction in the lower (bonding) band of the dimer structure and a repulsion in the upper (anti-bonding) band. Overcoming the onsite repulsion, this can lead to the appearance of superconductivity. The superconductivity depends strongly on the filling, and present a pairing structure more complex than s-wave pairing. Combining numerical and analytical methods such as the matrix product states ansatz, bosonization and perturbative calculations we map out the phase diagram of the two-leg ladder system and identify its superconducting phase. We characterize the transition from the non-density-assisted repulsive regime to the spin-gapped superconducting regime as a Berezinskii-Kosterlitz-Thouless transition.

LR-WaveHoltz: A Low-Rank Helmholtz Solver

Authors: Andreas Granath, Daniel Appelö, Siyang Wang

arXiv ID: 2510.09352 | Date: 2025-10-10

Abstract: We propose a low-rank method for solving the Helmholtz equation. Our approach is based on the WaveHoltz method, which computes Helmholtz solutions by applying a time-domain filter to the solution of a related wave equation. The wave equation is discretized by high-order multiblock summation-by-parts finite differences. In two dimensions we use the singular value decomposition and in three dimensions we use tensor trains to compress the numerical solution. To control rank growth we use step-truncation during time stepping and a low-rank Anderson acceleration for the WaveHoltz fixed point iteration. We have carried out extensive numerical experiments demonstrating the convergence and efficacy of the iterative scheme for free- and half-space problems in two and three dimensions with constant and piecewise constant wave speeds.

Mathematical aspects of the decomposition of diagonal U(N) operators

Authors: M. M. Fedin, A. A. Morozov

arXiv ID: 2510.11735 | Date: 2025-10-10

Abstract: We prove the decomposition of arbitrary diagonal operators into tensor and matrix products of smaller matrices, focusing on the analytic structure of the resulting formulas and their inherent symmetries. Diagrammatic representations are introduced, providing clear visualizations of the structure of these decompositions. We also discuss symmetries of the suggested decomposition. Methods and representations developed in this paper can be applied in different areas, including optimization of quantum computing algorithms, complex biological analysis, crystallography, optimization of AI models, and others.

The charge-singlet measurement toolbox

Authors: Abhijit Chakraborty, Randy Lewis, Christine A. Muschik

arXiv ID: 2510.08718 | Date: 2025-10-09

Abstract: Symmetry is fundamental to physical laws across different scales-from spacetime structure in general relativity to particle interactions in quantum field theory. Local symmetries, described by gauge theories, are central to phenomena such as superconductivity, topological phases, and the Standard Model of particle physics. Emerging simulation techniques using tensor network states or quantum computers offer exciting new possibilities of exploring the physics of these gauge theories, but require careful implementation of gauge symmetry and charge-neutrality constraints. This is especially challenging for non-Abelian gauge theories such as quantum chromodynamics (QCD), which governs the strong interaction between quarks and gluons. In a recent article (arXiv:2501.00579), we introduced "charge-singlet measurements" for quantum simulations, consisting of a projection based technique from group representation theory that allowed us to probe for the first time the phase diagram of (1+1)-dimensional QCD on a quantum computer. In this article, we show more broadly how to apply charge-singlet measurements as a flexible tool for both classical and quantum simulations of discrete and continuous gauge theories. Our approach extends the use of charge-singlet measurements beyond state preparation in the charge neutral (charge-singlet) sector to include noise mitigation in symmetry-preserving time-evolution circuits. We further demonstrate how this method enables the computation of thermodynamic observables-such as entropy-within the charge-singlet subspace, providing a new tool for exploring the connection between quantum thermodynamics and gauge symmetry.

Tensor-network representation of excitations in Josephson junction arrays

Authors: Emilio Rui, Joachim Cohen, Alexandru Petrescu

arXiv ID: 2510.08680 | Date: 2025-10-09

Abstract: We present a nonperturbative tensor-network approach to the excitation spectra of superconducting circuits based on Josephson junction arrays. These arrays provide the large lumped inductances required for qubit designs, yet their intrinsically many-body nature is typically reduced to effective single-mode descriptions. Perturbative treatments attempt to include the collective array modes neglected in these approximations, but a fully nonperturbative analysis is challenging due to the many-body structure and the collective character of these modes. We overcome this difficulty using the DMRG-X algorithm, which extends tensor-network methods to excited states. Our key advance is a construction of trial states from the linearized mode structure, enabling direct computation of excitations, even in degenerate manifolds, which was previously inaccessible. Our results reveal significant deviations from, and allow us to improve upon, previous perturbative treatments in the regime of low array junction impedance.

Tripartite entanglement in the HaPPY code is not holographic

Authors: Sriram Akella

arXiv ID: 2510.08520 | Date: 2025-10-09

Abstract: Holographic states satisfy several entropic inequalities owing to the Ryu-Takayangi formula. A drawback of these inequalities is that they only use bipartite entanglement in their formulation. We investigate a recently proposed "GHZ-forbidding" inequality, built out of the reflected entropy and the tripartite multi-entropy, that holds for holographic states. We show that the inequality is either violated or saturated, but never strictly satisfied, by stabilizer states, thereby showing that stabilizer states are not holographic. As a consequence, we show that tripartite entanglement in the HaPPY code is not holographic.

Randomized truncation of quantum states

Authors: Aram W. Harrow, Angus Lowe, Freek Witteveen

arXiv ID: 2510.08518 | Date: 2025-10-09

Abstract: A fundamental task in quantum information is to approximate a pure quantum state in terms of sparse states or, for a bipartite system, states of bounded Schmidt rank. The optimal deterministic approximation in each case is straightforward, and maximizes the fidelity: keep the largest entries or singular values. On the other hand, random mixtures of sparse states can achieve quadratically improved trace distances, and yield nontrivial bounds on other distance measures like the robustness. In this work, we give efficient algorithms for finding mixtures of sparse states that optimally approximate a given pure state in either trace distance or robustness. These algorithms also yield descriptions of efficiently samplable ensembles of sparse, or less-entangled, states that correspond to these optimal mixed approximations. This can be used for the truncation step of algorithms for matrix product states, improving their accuracy while using no extra memory, and we demonstrate this improvement numerically. Our proofs use basic facts about convex optimization and zero-sum games, as well as rigorous guarantees for computing maximum-entropy distributions.

Exponential Speed-ups for Structured Goemans-Williamson relaxations via Quantum Gibbs States and Pauli Sparsity

Authors: Haomu Yuan, Daniel Stilck França, Ilia Luchnikov, Egor Tiunov, Tobias Haug, Leandro Aolita

arXiv ID: 2510.08292 | Date: 2025-10-09

Abstract: Quadratic Unconstrained Binary Optimization (QUBO) problems are prevalent in various applications and are known to be NP-hard. The seminal work of Goemans and Williamson introduced a semidefinite programming (SDP) relaxation for such problems, solvable in polynomial time that upper bounds the optimal value. Their approach also enables randomized rounding techniques to obtain feasible solutions with provable performance guarantees. In this work, we identify instances of QUBO problems where matrix multiplicative weight methods lead to quantum and quantum-inspired algorithms that approximate the Goemans-Williamson SDP exponentially faster than existing methods, achieving polylogarithmic time complexity relative to the problem dimension. This speedup is attainable under the assumption that the QUBO cost matrix is sparse when expressed as a linear combination of Pauli strings satisfying certain algebraic constraints, and leverages efficient quantum and classical simulation results for quantum Gibbs states. We demonstrate how to verify these conditions efficiently given the decomposition. Additionally, we explore heuristic methods for randomized rounding procedures and extract the energy of a feasible point of the QUBO in polylogarithmic time. While the practical relevance of instances where our methods excel remains to be fully established, we propose heuristic algorithms with broader applicability and identify Kronecker graphs as a promising class for applying our techniques. We conduct numerical experiments to benchmark our methods. Notably, by utilizing tensor network methods, we solve an SDP with D=250D = 2^{50} variables and extract a feasible point which is certifiably within 0.15%0.15\% of the optimum of the QUBO through our approach on a desktop, reaching dimensions millions of times larger than those handled by existing SDP or QUBO solvers, whether heuristic or rigorous.

Hyper-optimized Quantum Lego Contraction Schedules

Authors: Balint Pato, June Vanlerberghe, Kenneth R. Brown

arXiv ID: 2510.08210 | Date: 2025-10-09

Abstract: Calculating the quantum weight enumerator polynomial (WEP) is a valuable tool for characterizing quantum error-correcting (QEC) codes, but it is computationally hard for large or complex codes. The Quantum LEGO (QL) framework provides a tensor network approach for WEP calculation, in some cases offering superpolynomial speedups over brute-force methods, provided the code exhibits area law entanglement, that a good QL layout is used, and an efficient tensor network contraction schedule is found. We analyze the performance of a hyper-optimized contraction schedule framework across QL layouts for diverse stabilizer code families. We find that the intermediate tensors in the QL networks for stabilizer WEPs are often highly sparse, invalidating the dense-tensor assumption of standard cost functions. To address this, we introduce an exact, polynomial-time Sparse Stabilizer Tensor (SST) cost function based on the rank of the parity check matrices for intermediate tensors. The SST cost function correlates perfectly with the true contraction cost, providing a significant advantage over the default cost function, which exhibits large uncertainty. Optimizing contraction schedules using the SST cost function yields substantial performance gains, achieving up to orders of magnitude improvement in actual contraction cost compared to using the dense tensor cost function. Furthermore, the precise cost estimation from the SST function offers an efficient metric to decide whether the QL-based WEP calculation is computationally superior to brute force for a given QL layout. These results, enabled by PlanqTN, a new open-source QL implementation, validate hyper-optimized contraction as a crucial technique for leveraging the QL framework to explore the QEC code design space.

Structured covariance estimation via tensor-train decomposition

Authors: Artsiom Patarusau, Nikita Puchkin, Maxim Rakhuba, Fedor Noskov

arXiv ID: 2510.08174 | Date: 2025-10-09

Abstract: We consider a problem of covariance estimation from a sample of i.i.d. high-dimensional random vectors. To avoid the curse of dimensionality we impose an additional assumption on the structure of the covariance matrix ΣΣ. To be more precise we study the case when ΣΣ can be approximated by a sum of double Kronecker products of smaller matrices in a tensor train (TT) format. Our setup naturally extends widely known Kronecker sum and CANDECOMP/PARAFAC models but admits richer interaction across modes. We suggest an iterative polynomial time algorithm based on TT-SVD and higher-order orthogonal iteration (HOOI) adapted to Tucker-2 hybrid structure. We derive non-asymptotic dimension-free bounds on the accuracy of covariance estimation taking into account hidden Kronecker product and tensor train structures. The efficiency of our approach is illustrated with numerical experiments.

Hamiltonian Decoded Quantum Interferometry

Authors: Alexander Schmidhuber, Jonathan Z. Lu, Noah Shutty, Stephen Jordan, Alexander Poremba, Yihui Quek

arXiv ID: 2510.07913 | Date: 2025-10-09

Abstract: We introduce Hamiltonian Decoded Quantum Interferometry (HDQI), a quantum algorithm that utilizes coherent Bell measurements and the symplectic representation of the Pauli group to reduce Gibbs sampling and Hamiltonian optimization to classical decoding. For a signed Pauli Hamiltonian HH and any degree-\ell polynomial P{P}, HDQI prepares a purification of the density matrix ρP(H)P2(H)ρ_{P}(H) \propto {P}^2(H) by solving a combination of two tasks: decoding \ell errors on a classical code defined by HH, and preparing a pilot state that encodes the anti-commutation structure of HH. Choosing P(x)P(x) to approximate exp(βx/2)\exp(-βx/2) yields Gibbs states at inverse temperature ββ; other choices prepare approximate ground states, microcanonical ensembles, and other spectral filters. For local Hamiltonians, the corresponding decoding problem is that of LDPC codes. Preparing the pilot state is always efficient for commuting Hamiltonians, but highly non-trivial for non-commuting Hamiltonians. Nevertheless, we prove that this state admits an efficient matrix product state representation for Hamiltonians whose anti-commutation graph decomposes into connected components of logarithmic size. We show that HDQI efficiently prepares Gibbs states at arbitrary temperatures for a class of physically motivated commuting Hamiltonians -- including the toric code and Haah's cubic code -- but we also develop a matching efficient classical algorithm for this task. For a non-commuting semiclassical spin glass and commuting stabilizer Hamiltonians with quantum defects, HDQI prepares Gibbs states up to a constant inverse-temperature threshold using polynomial quantum resources and quasi-polynomial classical pre-processing. These results position HDQI as a versatile algorithmic primitive and the first extension of Regev's reduction to non-abelian groups.

Efficient Closest Matrix Product State Learning in Logarithmic Depth

Authors: Chia-Ying Lin, Nai-Hui Chia, Shih-Han Hung

arXiv ID: 2510.07798 | Date: 2025-10-09

Abstract: Learning the closest matrix product state (MPS) representation of a quantum state is known to enable useful tools for prediction and analysis of complex quantum systems. In this work, we study the problem of learning MPS in following setting: given many copies of an input MPS, the task is to recover a classical description of the state. The best known polynomial-time algorithm, introduced by [LCLP10, CPF+10], requires linear circuit depth and O(n5)O(n^5) samples, and has seen no improvement in over a decade. The strongest known lower bound is only Ω(n)Ω(n). The combination of linear depth and high sample complexity renders existing algorithms impractical for near-term or even early fault-tolerant quantum devices. We show a new efficient MPS learning algorithm that runs in O(logn)O(\log n) depth and has sample complexity O(n3)O(n^3). Also, we can generalize our algorithm to learn closest MPS state, in which the input state is not guaranteed to be close to the MPS with a fixed bond dimension. Our algorithms also improve both sample complexity and circuit depth of previous known algorithm.

Correlation Lengths for Stochastic Matrix Product States

Authors: Lubashan Pathirana, Albert H. Werner

arXiv ID: 2510.07561 | Date: 2025-10-08

Abstract: We introduce a general model of stochastically generated matrix product states (MPS) in which the local tensors share a common distribution and form a strictly stationary sequence, without requiring spatial independence. Under natural conditions on the associated transfer operators, we prove the existence of thermodynamic limits of expectations of local observables and establish almost-sure exponential decay of two-point correlations. In the homogeneous (random translation-invariant) case, for any error tolerance in probability, the two-point function decays exponentially in the distance between the two sites, with a deterministic rate. In the i.i.d. case, the exponential decay still holds with a deterministic rate, with the probability approaching one exponentially fast in the distance. For strictly stationary ensembles with decaying spatial dependence, the correlation decay quantitatively reflects the mixing profile: (ρρ)-mixing yields polynomial bounds with high probability, while stretched-exponential (resp. exponential) decay in (ρρ) (resp. (ββ)) yields stretched-exponential (resp. exponential) decay of the two-point function, again with correspondingly strong high-probability guarantees. Altogether, the framework unifies and extends recent progress on stationary ergodic and Gaussian translation-invariant ensembles, providing a transfer-operator route to typical correlation decay in random MPS.

Dissipative Generation of Currents by Nonreciprocal Local and Global Environments

Authors: Catalin-Mihai Halati

arXiv ID: 2510.07498 | Date: 2025-10-08

Abstract: We investigate the mechanisms necessary for the stabilization of complex quantum correlations by exploring dissipative couplings to nonreciprocal reservoirs. We analyze the role of locality in the coupling between the environment and the quantum system of interest, as we consider either local couplings throughout the system, or a single global coupling. We contrast the results obtained for the two scenarios in which a chain of strongly interacting hardcore bosonic atoms is coupled directly to Markovian kinetic dissipative processes, or experiences effective dissipation through the mediation of the field of a lossy optical cavity. To investigate the dissipative dynamics of the many-body quantum systems considered we perform numerical simulations employing matrix product states methods. We show that by coupling atomic tunneling terms to the global field of a dissipative cavity we can stabilize at long times both finite currents and current-current correlations throughout the atomic chain. This is in contrast to the setup in which dissipation acts directly via local tunneling processes, where currents arise in a narrow region of the system and the current-current correlations are rapidly decaying.

Spectral properties and coding transitions of Haar-random quantum codes

Authors: Grace M. Sommers, J. Alexander Jacoby, Zack Weinstein, David A. Huse, Sarang Gopalakrishnan

arXiv ID: 2510.07396 | Date: 2025-10-08

Abstract: A quantum error-correcting code with a nonzero error threshold undergoes a mixed-state phase transition when the error rate reaches that threshold. We explore this phase transition for Haar-random quantum codes, in which the logical information is encoded in a random subspace of the physical Hilbert space. We focus on the spectrum of the encoded system density matrix as a function of the rate of uncorrelated, single-qudit errors. For low error rates, this spectrum consists of well-separated bands, representing errors of different weights. As the error rate increases, the bands for high-weight errors merge. The evolution of these bands with increasing error rate is well described by a simple analytic ansatz. Using this ansatz, as well as an explicit calculation, we show that the threshold for Haar-random quantum codes saturates the hashing bound, and thus coincides with that for random \emph{stabilizer} codes. For error rates that exceed the hashing bound, typical errors are uncorrectable, but postselected error correction remains possible until a much higher \emph{detection} threshold. Postselection can in principle be implemented by projecting onto subspaces corresponding to low-weight errors, which remain correctable past the hashing bound.

Tangent space Krylov computation of real-frequency spectral functions: Influence of density-assisted hopping on 2D Mott physics

Authors: Oleksandra Kovalska, Jan von Delft, Andreas Gleis

arXiv ID: 2510.07279 | Date: 2025-10-08

Abstract: We present a tangent-space Krylov (TaSK) method for efficient computation of zero-temperature real-frequency spectral functions on top of ground state (GS) matrix product states (MPS) obtained from the Density Matrix Renormalization Group. It relies on projecting resolvents to the tangent space of the GS-MPS, where they can be efficiently represented using Krylov space techniques. This allows for a direct computation of spectral weights and their corresponding positions on the real-frequency axis. We demonstrate the accuracy and efficiency of the TaSK approach by showcasing spectral data for various models. These include the 1D Haldane-Shastry and Heisenberg models as benchmarks. As an interesting application, we study the Hubbard model on a cylinder at half-filling, augmented by a density-assisted hopping (DAH) term. We find that DAH leads to particle-hole asymmetric single-particle mobilities and lifetimes in the resulting Mott insulator, and identify the responsible scattering processes. Further, we find that DAH influences the dispersion of Green's function zeros beyond its range, which has a frustrating effect on the Mott insulator studied here.

Efficient tensor-network simulations of weakly-measured quantum circuits

Authors: Darren Pereira, Leonardo Banchi

arXiv ID: 2510.07211 | Date: 2025-10-08

Abstract: We present a tensor-network-based method for simulating a weakly-measured quantum circuit. In particular, we use a Markov chain to efficiently sample measurements and contract the tensor network, propagating their effect forward along the spatial direction. Applications of our algorithm include validating quantum computers (capable of mid-circuit measurements) in regimes of easy classical simulability, and studying generative-machine-learning applications, where sampling from complex stochastic processes is the main task. As a demonstration of our algorithm, we consider a (1+1)-dimensional brickwall circuit of Haar-random unitaries, interspersed with generalized single-qubit measurements of variable strength. We simulate the dynamics for tens to hundreds of qubits if the circuit exhibits area-law entanglement (under strong measurements), and tens of qubits if it exhibits volume-law entanglement (under weak measurements). We observe signatures of a measurement-induced phase transition between the two regimes as a function of measurement strength.

Preparation of initial states with open and periodic boundary conditions on quantum devices using matrix product states

Authors: Yibin Guo, Manuel Schneider, Takis Angelides, Karl Jansen, C. -J. David Lin, Yao Ting Su

arXiv ID: 2510.07125 | Date: 2025-10-08

Abstract: We present a framework for preparing quantum states from matrix product states (MPS) with open and periodic boundary conditions on quantum devices. The MPS tensors are mapped to unitary gates, which are subsequently decomposed into native gates on quantum hardware. States with periodic boundary conditions (pbc) can be represented efficiently as quantum circuits using ancilla qubits and post-selection after measurement. We derive an exact expression for the success rate of this probabilistic approach, which can be evaluated a priori. The applicability of the method is demonstrated in two examples. First, we prepare the ground state of the Heisenberg model with pbc and simulate dynamics under a quenched Hamiltonian. The volume-law entanglement growth in the time evolution challenges classical algorithms but can potentially be overcome on quantum hardware. Second, we construct quantum circuits that generate excited states of the Schwinger model with high fidelities. Our approach provides a scalable method for preparing states on a quantum device, enabling efficient simulations of strongly correlated systems on near-term quantum computers.

Preparation of initial states with open and periodic boundary conditions on quantum devices using matrix product states

Authors: Yibin Guo, Manuel Schneider, Takis Angelides, Karl Jansen, C. -J. David Lin, Yao Ting Su

arXiv ID: 2510.07125 | Date: 2025-10-08

Abstract: We present a framework for preparing quantum states from matrix product states (MPS) with open and periodic boundary conditions on quantum devices. The MPS tensors are mapped to unitary gates, which are subsequently decomposed into native gates on quantum hardware. States with periodic boundary conditions (pbc) can be represented efficiently as quantum circuits using ancilla qubits and post-selection after measurement. We derive an exact expression for the success rate of this probabilistic approach, which can be evaluated a priori. The applicability of the method is demonstrated in two examples. First, we prepare the ground state of the Heisenberg model with pbc and simulate dynamics under a quenched Hamiltonian. The volume-law entanglement growth in the time evolution challenges classical algorithms but can potentially be overcome on quantum hardware. Second, we construct quantum circuits that generate excited states of the Schwinger model with high fidelities. Our approach provides a scalable method for preparing states on a quantum device, enabling efficient simulations of strongly correlated systems on near-term quantum computers.

Simulating Topological Order on Quantum Processors

Authors: Adam Gammon-Smith, Michael Knap, Frank Pollmann

arXiv ID: 2510.07023 | Date: 2025-10-08

Abstract: It is an ongoing quest to realize topologically ordered quantum states on different platforms including condensed matter systems, quantum simulators and digital quantum processors. Unlike conventional states characterized by their local order, these exotic states are characterized by their non-local entanglement. The consequences of topological order can be as profound as they are surprising, ranging from the emergence of fractionalized anyonic excitations to potentially providing a scalable platform for quantum error correction. This deep connection to quantum computing naturally motivates the realization and study of topologically ordered quantum states on quantum processors. However, due to the non-local nature of these states, their study presents a challenge for near-term quantum devices. This Perspective aims to review the recent progress towards the experimental realization of topologically ordered quantum states, their potential applications, and promising directions of future research.

Fisher Information, Training and Bias in Fourier Regression Models

Authors: Lorenzo Pastori, Veronika Eyring, Mierk Schwabe

arXiv ID: 2510.06945 | Date: 2025-10-08

Abstract: Motivated by the growing interest in quantum machine learning, in particular quantum neural networks (QNNs), we study how recently introduced evaluation metrics based on the Fisher information matrix (FIM) are effective for predicting their training and prediction performance. We exploit the equivalence between a broad class of QNNs and Fourier models, and study the interplay between the \emph{effective dimension} and the \emph{bias} of a model towards a given task, investigating how these affect the model's training and performance. We show that for a model that is completely agnostic, or unbiased, towards the function to be learned, a higher effective dimension likely results in a better trainability and performance. On the other hand, for models that are biased towards the function to be learned a lower effective dimension is likely beneficial during training. To obtain these results, we derive an analytical expression of the FIM for Fourier models and identify the features controlling a model's effective dimension. This allows us to construct models with tunable effective dimension and bias, and to compare their training. We furthermore introduce a tensor network representation of the considered Fourier models, which could be a tool of independent interest for the analysis of QNN models. Overall, these findings provide an explicit example of the interplay between geometrical properties, model-task alignment and training, which are relevant for the broader machine learning community.

Expressive and Scalable Quantum Fusion for Multimodal Learning

Authors: Tuyen Nguyen, Trong Nghia Hoang, Phi Le Nguyen, Hai L. Vu, Truong Cong Thang

arXiv ID: 2510.06938 | Date: 2025-10-08

Abstract: The aim of this paper is to introduce a quantum fusion mechanism for multimodal learning and to establish its theoretical and empirical potential. The proposed method, called the Quantum Fusion Layer (QFL), replaces classical fusion schemes with a hybrid quantum-classical procedure that uses parameterized quantum circuits to learn entangled feature interactions without requiring exponential parameter growth. Supported by quantum signal processing principles, the quantum component efficiently represents high-order polynomial interactions across modalities with linear parameter scaling, and we provide a separation example between QFL and low-rank tensor-based methods that highlights potential quantum query advantages. In simulation, QFL consistently outperforms strong classical baselines on small but diverse multimodal tasks, with particularly marked improvements in high-modality regimes. These results suggest that QFL offers a fundamentally new and scalable approach to multimodal fusion that merits deeper exploration on larger systems.

Randomized Quantum Singular Value Transformation

Authors: Xinzhao Wang, Yuxin Zhang, Soumyabrata Hazra, Tongyang Li, Changpeng Shao, Shantanav Chakraborty

arXiv ID: 2510.06851 | Date: 2025-10-08

Abstract: We introduce the first randomized algorithms for Quantum Singular Value Transformation (QSVT), a unifying framework for many quantum algorithms. Standard implementations of QSVT rely on block encodings of the Hamiltonian, which are costly to construct, requiring a logarithmic number of ancilla qubits, intricate multi-qubit control, and circuit depth scaling linearly with the number of Hamiltonian terms. In contrast, our algorithms use only a single ancilla qubit and entirely avoid block encodings. We develop two methods: (i) a direct randomization of QSVT, where block encodings are replaced by importance sampling, and (ii) an approach that integrates qDRIFT into the generalized quantum signal processing framework, with the dependence on precision exponentially improved through classical extrapolation. Both algorithms achieve gate complexity independent of the number of Hamiltonian terms, a hallmark of randomized methods, while incurring only quadratic dependence on the degree of the target polynomial. We identify natural parameter regimes where our methods outperform even standard QSVT, making them promising for early fault-tolerant quantum devices. We also establish a fundamental lower bound showing that the quadratic dependence on the polynomial degree is optimal within this framework. We apply our framework to two fundamental tasks: solving quantum linear systems and estimating ground-state properties of Hamiltonians, obtaining polynomial advantages over prior randomized algorithms. Finally, we benchmark our ground-state property estimation algorithm on electronic structure Hamiltonians and the transverse-field Ising model with long-range interactions. In both cases, our approach outperforms prior work by several orders of magnitude in circuit depth, establishing randomized QSVT as a practical and resource-efficient alternative for early fault-tolerant quantum devices.

On the complexity of estimating ground state entanglement and free energy

Authors: Sevag Gharibian, Jonas Kamminga

arXiv ID: 2510.06796 | Date: 2025-10-08

Abstract: Understanding the entanglement structure of local Hamiltonian ground spaces is a physically motivated problem, with applications ranging from tensor network design to quantum error-correcting codes. To this end, we study the complexity of estimating ground state entanglement, and more generally entropy estimation for low energy states and Gibbs states. We find, in particular, that the classes qq-QAM [Kobayashi, le Gall, Nishimura, SICOMP 2019] (a quantum analogue of public-coin AM) and QMA(2) (QMA with unentangled proofs) play a crucial role for such problems, showing: (1) Detecting a high-entanglement ground state is qq-QAM-complete, (2) computing an additive error approximation to the Helmholtz free energy (equivalently, a multiplicative error approximation to the partition function) is in qq-QAM, (3) detecting a low-entanglement ground state is QMA(2)-hard, and (4) detecting low energy states which are close to product states can range from QMA-complete to QMA(2)-complete. Our results make progress on an open question of [Bravyi, Chowdhury, Gosset and Wocjan, Nature Physics 2022] on free energy, and yield the first QMA(2)-complete Hamiltonian problem using local Hamiltonians (cf. the sparse QMA(2)-complete Hamiltonian problem of [Chailloux, Sattath, CCC 2012]).

Breaking the Treewidth Barrier in Quantum Circuit Simulation with Decision Diagrams

Authors: Bin Cheng, Ziyuan Wang, Ruixuan Deng, Jianxin Chen, Zhengfeng Ji

arXiv ID: 2510.06775 | Date: 2025-10-08

Abstract: Classical simulation of quantum circuits is a critical tool for validating quantum hardware and probing the boundary between classical and quantum computational power. Existing state-of-the-art methods, notably tensor network approaches, have computational costs governed by the treewidth of the underlying circuit graph, making circuits with large treewidth intractable. This work rigorously analyzes FeynmanDD, a decision diagram-based simulation method proposed in CAV 2025 by a subset of the authors, and shows that the size of the multi-terminal decision diagram used in FeynmanDD is exponential in the linear rank-width of the circuit graph. As linear rank-width can be substantially smaller than treewidth and is at most larger than the treewidth by a logarithmic factor, our analysis demonstrates that FeynmanDD outperforms all tensor network-based methods for certain circuit families. We also show that the method remains efficient if we use the Solovay-Kitaev algorithm to expand arbitrary single-qubit gates to sequences of Hadamard and T gates, essentially removing the gate-set restriction posed by the method.

Phase structure analysis of 2d lattice CP(1) model with θθ term using tensor renormalization group method

Authors: Hayato Aizawa, Shinji Takeda, Yusuke Yoshimura

arXiv ID: 2510.06624 | Date: 2025-10-08

Abstract: We investigate the phase structure of a two-dimensional lattice CP(1) model with a θθ term. In particular, we aim to identify a critical region expected to exist along a θ=πθ=π line. To explore the phase structure non-perturbatively and avoid the sign problem, we employ the tensor renormalization group method. We make two improvements compared to previous tensor network studies. The first improvement involves refining the initial tensor. Specifically, we construct it using a quadrature method, which achieves higher accuracy compared to the conventional approach. The second improvement consists of analyzing the phase structure using the information of the conformal field theory, namely the central charge and the scaling dimensions, which can be accessed relatively easily via the tensor renormalization group method. Thanks to these improvements, we identify both the onset of the critical region, βc=0.5952(8)β_{\rm c}=0.5952(8) and its universality class as the SU(2)k=1{}_{k=1} Wess-Zumino-Witten model.

Hyperinvariant Spin Network States -- An AdS/CFT Model from First Principles

Authors: Fynn Otto, Refik Mansuroglu, Norbert Schuch, Otfried Gühne, Hanno Sahlmann

arXiv ID: 2510.06602 | Date: 2025-10-08

Abstract: We study the existence and limitations for hyperinvariant tensor networks incorporating a local SU(2) symmetry. As discrete implementations of the anti de-Sitter/conformal field theory (AdS/CFT) correspondence, such networks have created bridges between the fields of quantum information theory and quantum gravity. Adding SU(2) symmetry to the tensor network allows a direct connection to spin network states, a basis of the kinematic Hilbert space of loop quantum gravity (LQG). We consider a particular situation where the states can be interpreted as kinematic quantum states for three-dimensional quantum gravity. We show that important aspects of the AdS/CFT correspondence are realized in certain quantum states of the gravitational field in LQG, thus justifying, from first principles, a class of models introduced by [F. Pastawski et al., JHEP 06, 149 (2015)]. We provide examples of hyperinvariant tensor networks, but also prove constraints on their existence in the form of no-go theorems that exclude absolutely maximally entangled states as well as general holographic codes from local SU(2)-invariance. We calculate surface areas as expectation values of the LQG area operator and discuss further possible constraints as a consequence of a decay of correlations on the boundary.

Approximate maximum likelihood decoding with KK minimum weight matchings

Authors: Mao Lin

arXiv ID: 2510.06531 | Date: 2025-10-08

Abstract: The minimum weight matching (MWM) and maximum likelihood decoding (MLD) are two widely used and distinct decoding strategies for quantum error correction. For a given syndrome, the MWM decoder finds the most probable physical error corresponding to the MWM of the decoding graph, whereas MLD aims to find the most probable logical error. Although MLD is the optimal error correction strategy, it is typically more computationally expensive compared to the MWM decoder. In this work, we introduce an algorithm that approximates MLD with KK MWMs from the decoding graph. Taking the surface code subject to graphlike errors as an example, we show that it is possible to efficiently find the first KK MWMs by systematically modifying the original decoding graph followed by finding the MWMs of the modified graphs. For the case where the XX and ZZ errors are correlated, despite the MWM of the decoding hypergraph cannot be found efficiently, we present a heuristic approach to approximate the MLD by finding the KK MWMs in the XX and ZZ subgraphs. We benchmark the efficacy of our algorithm for the surface code subject to graphlike errors, the surface-square Gottesman-Kitaev-Preskill (GKP) code and surface-hexagonal GKP code subject to the Gaussian random displacement errors, showing that the fidelity approaches that of the exact MLD (for the first two cases) or the tensor-network decoder (for the last case) as KK increases.

Diffusion-Guided Renormalization of Neural Systems via Tensor Networks

Authors: Nathan X. Kodama

arXiv ID: 2510.06361 | Date: 2025-10-07

Abstract: Far from equilibrium, neural systems self-organize across multiple scales. Exploiting multiscale self-organization in neuroscience and artificial intelligence requires a computational framework for modeling the effective non-equilibrium dynamics of stochastic neural trajectories. Non-equilibrium thermodynamics and representational geometry offer theoretical foundations, but we need scalable data-driven techniques for modeling collective properties of high-dimensional neural networks from partial subsampled observations. Renormalization is a coarse-graining technique central to studying emergent scaling properties of many-body and nonlinear dynamical systems. While widely applied in physics and machine learning, coarse-graining complex dynamical networks remains unsolved, affecting many computational sciences. Recent diffusion-based renormalization, inspired by quantum statistical mechanics, coarse-grains networks near entropy transitions marked by maximal changes in specific heat or information transmission. Here I explore diffusion-based renormalization of neural systems by generating symmetry-breaking representations across scales and offering scalable algorithms using tensor networks. Diffusion-guided renormalization bridges microscale and mesoscale dynamics of dissipative neural systems. For microscales, I developed a scalable graph inference algorithm for discovering community structure from subsampled neural activity. Using community-based node orderings, diffusion-guided renormalization generates renormalization group flow through metagraphs and joint probability functions. Towards mesoscales, diffusion-guided renormalization targets learning the effective non-equilibrium dynamics of dissipative neural trajectories occupying lower-dimensional subspaces, enabling coarse-to-fine control in systems neuroscience and artificial intelligence.

Classical simulation of noisy random circuits from exponential decay of correlation

Authors: Su-un Lee, Soumik Ghosh, Changhun Oh, Kyungjoo Noh, Bill Fefferman, Liang Jiang

arXiv ID: 2510.06328 | Date: 2025-10-07

Abstract: We study the classical simulability of noisy random quantum circuits under general noise models. While various classical algorithms for simulating noisy random circuits have been proposed, many of them rely on the anticoncentration property, which can fail when the circuit depth is small or under realistic noise models. We propose a new approach based on the exponential decay of conditional mutual information (CMI), a measure of tripartite correlations. We prove that exponential CMI decay enables a classical algorithm to sample from noisy random circuits -- in polynomial time for one dimension and quasi-polynomial time for higher dimensions -- even when anticoncentration breaks down. To this end, we show that exponential CMI decay makes the circuit depth effectively shallow, and it enables efficient classical simulation for sampling. We further provide extensive numerical evidence that exponential CMI decay is a universal feature of noisy random circuits across a wide range of noise models. Our results establish CMI decay, rather than anticoncentration, as the fundamental criterion for classical simulability, and delineate the boundary of quantum advantage in noisy devices.

An efficient algorithm to compute entanglement in states with low magic

Authors: ChunJun Cao, Gong Cheng, Tianci Zhou

arXiv ID: 2510.06318 | Date: 2025-10-07

Abstract: A bottleneck for analyzing the interplay between magic and entanglement is the computation of these quantities in highly entangled quantum many-body magic states. Efficient extraction of entanglement can also inform our understanding of dynamical quantum processes such as measurement-induced phase transition and approximate unitary designs. We develop an efficient classical algorithm to compute the von Neumann entropy and entanglement spectrum for such states under the condition that they have low stabilizer nullity. The algorithm exploits the property of stabilizer codes to separate entanglement into two pieces: one generated by the common stabilizer group and the other from the logical state. The low-nullity constraint ensures both pieces can be computed efficiently. Our algorithm can be applied to study the entanglement in sparsely TT-doped circuits with possible Pauli measurements as well as certain classes of states that have both high entanglement and magic. Combining with stabilizer learning subroutines, it also enables the efficient learning of von Neumann entropies for low-nullity states prepared on quantum devices.

Commensurate-incommensurate Mott transition without magnetic field: emergence of nematic Luttinger liquid in XXZ chain

Authors: Julien Fitouchi, Natalia Chepiga

arXiv ID: 2510.05988 | Date: 2025-10-07

Abstract: We investigate the zero-magnetization phase diagram of a spin-1/2 chain with competing ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor exchange couplings in the strongly interacting regime. Using density matrix renormalization group (DMRG) simulations, we discover two successive commensurate-incommensurate transitions of the non-conformal Pokrovsky-Talapov universality class, occurring (even) at zero magnetic field. The first transition marks the condensation of bound pairs of magnons into a critical phase with central charge c=2c=2, emerging from a gapped period-4 phase. At the second transition, an incommensurate quadrupolar (or nematic) Luttinger liquid forms out of a gapped phase separation state, via the pairwise condensation of domain walls. We argue that both transitions involve the same underlying incommensurate nematic Luttinger liquid, and that the c=2c=2 phase can be understood as a coexistence of a conventional (single-magnon type) and quadrupolar (two-magnon type) Luttinger liquids. Our results demonstrate that frustration alone is sufficient to drive continuous commensurate-incommensurate transitions of Mott type and stabilise incommensurate quasi-long-range order without doping.

Tensor Network Loop Cluster Expansions for Quantum Many-Body Problems

Authors: Johnnie Gray, Gunhee Park, Glen Evenbly, Nicola Pancotti, Eirik F. Kjønstad, Garnet Kin-Lic Chan

arXiv ID: 2510.05647 | Date: 2025-10-07

Abstract: We analyze the tensor network loop cluster expansion, introduced in arXiv:2504.07344 as a systematic correction to belief propagation, in the context of general quantum many-body problems. We provide numerical examples of the accuracy and practical applicability of the approach for the computation of ground-state observables for high bond dimension tensor networks, in two- and three-dimensions, with open and periodic boundary conditions, and for spin and fermion problems.

TeMFpy: a Python library for converting fermionic mean-field states into tensor networks

Authors: Simon H. Hille, Attila Szabó

arXiv ID: 2510.05227 | Date: 2025-10-06

Abstract: We introduce TeMFpy, a Python library for converting fermionic mean-field states to finite or infinite matrix product state (MPS) form. TeMFpy includes new, efficient, and easy-to-understand algorithms for both Slater determinants and Pfaffian states. Together with Gutzwiller projection, these also allow the user to build variational wave functions for various strongly correlated electron systems, such as quantum spin liquids. We present all implemented algorithms in detail and describe how they can be accessed through TeMFpy, including full example workflows. TeMFpy is built on top of TeNPy and, therefore, integrates seamlessly with existing MPS-based algorithms.

Variational optimization of projected entangled-pair states on the triangular lattice

Authors: Jan Naumann, Jens Eisert, Philipp Schmoll

arXiv ID: 2510.04907 | Date: 2025-10-06

Abstract: We introduce a general corner transfer matrix renormalization group algorithm tailored to projected entangled-pair states on the triangular lattice. By integrating automatic differentiation, our approach enables direct variational energy minimization on this lattice geometry. In contrast to conventional approaches that map the triangular lattice onto a square lattice with diagonal next-nearest-neighbour interactions, our native formulation yields improved variational results at the same bond dimension. This improvement stems from a more faithful and physically informed representation of the entanglement structure in the tensor network and an increased number of variational parameters. We apply our method to the antiferromagnetic nearest-neighbour Heisenberg model on the triangular and kagome lattice, and benchmark our results against previous numerical studies.

Mixed-precision ab initio tensor network state methods adapted for NVIDIA Blackwell technology via emulated FP64 arithmetic

Authors: Cole Brower, Samuel Rodriguez Bernabeu, Jeff Hammond, John Gunnels, Sotiris S. Xanthea, Martin Ganahl, Andor Menczer, Örs Legeza

arXiv ID: 2510.04795 | Date: 2025-10-06

Abstract: We report cutting-edge performance results via mixed-precision spin adapted ab initio Density Matrix Renormalization Group (DMRG) electronic structure calculations utilizing the Ozaki scheme for emulating FP64 arithmetic through the use of fixed-point compute resources. By approximating the underlying matrix and tensor algebra with operations on a modest number of fixed-point representatives (``slices''), we demonstrate on smaller benchmark systems and for the active compounds of the FeMoco and cytochrome P450 (CYP) enzymes with complete active space (CAS) sizes of up to 113 electrons in 76 orbitals [CAS(113, 76)] and 63 electrons in 58 orbitals [CAS(63, 58)], respectively, that the chemical accuracy can be reached with mixed-precision arithmetic. We also show that, due to its variational nature, DMRG provides an ideal tool to benchmark accuracy domains, as well as the performance of new hardware developments and related numerical libraries. Detailed numerical error analysis and performance assessment are also presented for subcomponents of the DMRG algebra by systematically interpolating between double- and pseudo-half-precision. Our analyis represents the first quantum chemistry evaluation of FP64 emulation for correlated calculations capable of achieving chemical accuracy and emulation based on fixed-point arithmetic, and it paves the way for the utilization of state-of-the-art Blackwell technology in tree-like tensor network state electronic structure calculations, opening new research directions in materials sciences and beyond.

Finite temperature dopant-induced spin reorganization explored via tensor networks in the two-dimensional tt-JJ model

Authors: Yintai Zhang, Aritra Sinha, Marek M. Rams, Jacek Dziarmaga

arXiv ID: 2510.04756 | Date: 2025-10-06

Abstract: Doped Mott insulators host intertwined spin-charge phenomena that evolve with temperature and can culminate in stripe order or superconductivity at low temperatures. The two-dimensional tt-JJ model captures this interplay yet finite-temperature, infinite-size calculations remain difficult. Using purification represented by a tensor network - an infinite projected entangled-pair state (iPEPS) ansatz - we simulate the tt-JJ model at finite temperature directly in the thermodynamic limit, reaching temperatures down to one tenth of the hopping rate and hole concentrations up to one quarter of the lattice sites. Beyond specific heat, uniform susceptibility, and compressibility, we introduce dopant-conditioned multi-point correlators that map how holes reshape local exchange. Nearest-neighbor hole pairs produce a strong cooperative response that reinforces antiferromagnetism on the adjacent parallel bonds, and single holes weaken nearby antiferromagnetic bonds; d-wave pairing correlations remain short-ranged over the same window. These results provide experiment-compatible thermodynamic-limit benchmarks and establish dopant-conditioned correlators as incisive probes of short-range spin-texture reorganization at finite temperature.

Clifford Circuits Augmented Grassmann Matrix Product States

Authors: Atis Yosprakob, Wei-Lin Tu, Tsuyoshi Okubo, Kouichi Okunishi, Donghoon Kim

arXiv ID: 2510.04164 | Date: 2025-10-05

Abstract: Recent advances in combining Clifford circuits with tensor network (TN) states have shown that classically simulable disentanglers can significantly reduce entanglement, mitigating the bond-dimension bottleneck in TN simulations. In this work, we develop a variational TN framework based on Grassmann tensor networks, which natively encode fermionic statistics while preserving locality. By incorporating locally defined Clifford circuits within the fermionic formalism, we simulate benchmark models including the tight-binding and tt-VV models. Our results show that Clifford disentangling removes the classically simulable component of entanglement, leading to a reduced bond dimension and improved accuracy in ground-state energy estimates. Interestingly, imposing the natural Grassmann-evenness constraint on the Clifford circuits significantly reduces the number of disentangling gates, from 720 to just 32, yielding a far more efficient implementation. These findings highlight the potential of Clifford-augmented Grassmann TNs as a scalable and accurate tool for studying strongly correlated fermionic systems, particularly in higher dimensions.

Operator dependence and robustness of spacetime-localized response in a quantum critical spin chain

Authors: Daichi Imagawa, Keiju Murata, Daisuke Yamamoto

arXiv ID: 2510.04047 | Date: 2025-10-05

Abstract: We investigate the phenomenon of spacetime-localized response in a quantum critical spin system, with particular attention to how it depends on the spatial profile and operator content of the applied perturbation, as well as its robustness against increase of amplitude and temporal discretization. Motivated by recent theoretical proposals linking such response patterns to the anti-de Sitter/conformal field theory correspondence, we numerically analyze the real-time dynamics of the one-dimensional transverse-field Ising model at criticality using the time-evolving block decimation algorithm. We find that sharply localized and periodically recurring responses emerge only for specific types of perturbations, namely those that correspond to local density fields in the continuum limit. In contrast, perturbations involving other spin components produce conventional propagating excitations without localization. Furthermore, we demonstrate that the response remains qualitatively robust when the time-dependent perturbation is approximated by a piecewise-linear function, highlighting the practical relevance of our findings for quantum simulation platforms with limited temporal resolution. Our results clarify the operator dependence of emergent bulk-like dynamics in critical spin chains and offer guidance for probing holographic physics in experimental settings.

Lattice Translation Modulated Symmetries and TFTs

Authors: Ching-Yu Yao

arXiv ID: 2510.03889 | Date: 2025-10-04

Abstract: Modulated symmetries are internal symmetries that are not invariant under spacetime symmetry actions. We propose a general way to describe the lattice translation modulated symmetries in 1+1D, including the non-invertible ones, via the tensor network language. We demonstrate that the modulations can be described by some autoequivalences of the categories. Although the topological behaviors are broken because of the presence of modulations, we can still construct the modulated version of the symmetry TFT bulks by inserting a series of domain walls described by invertible bimodule categories. This structure not only recovers some known results on invertible modulated symmetries but also provides a general framework to tackle modulated symmetries in a more general setting.

Congestion bounds via Laplacian eigenvalues and their application to tensor networks with arbitrary geometry

Authors: Sayan Mukherjee, Shinichiro Akiyama

arXiv ID: 2510.02725 | Date: 2025-10-03

Abstract: Embedding the vertices of arbitrary graphs into trees while minimizing some measure of overlap is an important problem with applications in computer science and physics. In this work, we consider the problem of bijectively embedding the vertices of an nn-vertex graph GG into the leaves of an nn-leaf rooted binary tree B\mathcal{B}. The congestion of such an embedding is given by the largest size of the cut induced by the two components obtained by deleting any vertex of B\mathcal{B}. The congestion cng(G)\mathrm{cng}(G) is defined as the minimum congestion obtained by any embedding. We show that λ2(G)2n/9cng(G)λn(G)2n/9λ_2(G)\cdot 2n/9\le \mathrm{cng} (G)\le λ_n(G)\cdot 2n/9, where 0=λ1(G)λn(G)0=λ_1(G)\le \cdots \le λ_n(G) are the Laplacian eigenvalues of GG. We also provide a contraction heuristic given by hierarchically spectral clustering the original graph, which we numerically find to be effective in finding low congestion embeddings for sparse graphs. We numerically compare our congestion bounds on different families of graphs with regular structure (hypercubes and lattices), random graphs, and tensor network representations of quantum circuits. Our results imply lower and upper bounds on the memory complexity of tensor network contraction in terms of the underlying graph.

Utility-Scale Quantum State Preparation: Classical Training using Pauli Path Simulation

Authors: Cheng-Ju Lin, Hrant Gharibyan, Vincent P. Su

arXiv ID: 2510.02428 | Date: 2025-10-02

Abstract: We use Pauli Path simulation to variationally obtain parametrized circuits for preparing ground states of various quantum many-body Hamiltonians. These include the quantum Ising model in one dimension, in two dimensions on square and heavy-hex lattices, and the Kitaev honeycomb model, all at system sizes of one hundred qubits or more, beyond the reach of exact state-vector simulation, thereby reaching utility scale. We benchmark the Pauli Path simulation results against exact ground-state energies when available, and against density-matrix renormalization group calculations otherwise, finding strong agreement. To further assess the quality of the variational states, we evaluate the magnetization in the x and z directions for the quantum Ising models and compute the topological entanglement entropy for the Kitaev honeycomb model. Finally, we prepare approximate ground states of the Kitaev honeycomb model with 48 qubits, in both the gapped and gapless regimes, on Quantinuum's System Model H2 quantum computer using parametrized circuits obtained from Pauli Path simulation. We achieve a relative energy error of approximately 5%5\% without error mitigation and demonstrate the braiding of Abelian anyons on the quantum device beyond fixed-point models.

Beyond Belief Propagation: Cluster-Corrected Tensor Network Contraction with Exponential Convergence

Authors: Siddhant Midha, Yifan F. Zhang

arXiv ID: 2510.02290 | Date: 2025-10-02

Abstract: Tensor network contraction on arbitrary graphs is a fundamental computational challenge with applications ranging from quantum simulation to error correction. While belief propagation (BP) provides a powerful approximation algorithm for this task, its accuracy limitations are poorly understood and systematic improvements remain elusive. Here, we develop a rigorous theoretical framework for BP in tensor networks, leveraging insights from statistical mechanics to devise a \emph{cluster expansion} that systematically improves the BP approximation. We prove that the cluster expansion converges exponentially fast if an object called the \emph{loop contribution} decays sufficiently fast with the loop size, giving a rigorous error bound on BP. We also provide a simple and efficient algorithm to compute the cluster expansion to arbitrary order. We demonstrate the efficacy of our method on the two-dimensional Ising model, where we find that our method significantly improves upon BP and existing corrective algorithms such as loop series expansion. Our work opens the door to a systematic theory of BP for tensor networks and its applications in decoding classical and quantum error-correcting codes and simulating quantum systems.

Fate of entanglement in open quantum spin liquid: Time evolution of its genuine multipartite negativity upon sudden coupling to a dissipative bosonic environment

Authors: Federico Garcia-Gaitan, Branislav K. Nikolic

arXiv ID: 2510.02256 | Date: 2025-10-02

Abstract: Topological properties of many-body entanglement in quantum spin liquids (QSLs), persisting at arbitrarily long distances, have been intensely explored over the past two decades, but mostly for QSLs viewed as {\em closed} quantum systems. However, in experiments and potential quantum computing applications, candidate materials for this exotic phase of quantum matter will always interact with a dissipative environment, such as the one generated by bosonic quasiparticles in solids at finite temperature. Here we investigate the spatial structure and stability of entanglement in the Kitaev model of QSL made {\em open} by sudden coupling to an infinite bosonic bath of Caldeira-Leggett type and time-evolved using the Lindblad quantum master equation in the Markovian regime (i.e., for weak coupling) or tensor network methods for open quantum systems in the non-Markovian regime (i.e., for strong coupling). From the time-evolved density matrix of QSL and its subregions, we extract genuine multipartite negativity (GMN), quantum Fisher information, spin-spin correlators, and expectation value (EV) of the Wilson loop operator. In particular, time-dependence of GMN offers the most penetrating insights: (i) in the Markovian regime, it remains non-zero in larger loopy subregions of QSL (as also discovered very recently for closed QSLs) up to temperatures comparable to Kitaev exchange interaction at which other quantities, such as EV of the Wilson loop operator, vanish; (ii) in the non-Markovian regime with pronounced memory effects, GMN remains non-zero up to even higher temperatures, while also acquiring non-zero value in smaller non-loopy subregions. The non-Markovian dynamics can also generate emergent interactions between spins, thereby opening avenues for tailoring properties of QSL via environmental engineering.

Variational approach to open quantum systems with long-range competing interactions

Authors: Dawid A. Hryniuk, Marzena H. Szymańska

arXiv ID: 2510.01543 | Date: 2025-10-02

Abstract: Competition between short- and long-range interactions underpins many emergent phenomena in nature. Despite rapid progress in their experimental control, computational methods capable of accurately simulating open quantum many-body systems with complex long-ranged interactions at scale remain scarce. Here, we address this limitation by introducing an efficient and scalable approach to dissipative quantum lattices in one and two dimensions, combining matrix product operators and time-dependent variational Monte Carlo. We showcase the versatility, effectiveness, and unique methodological advantages of our algorithm by simulating the non-equilibrium dynamics and steady states of spin-12\frac{1}{2} lattices with competing algebraically-decaying interactions for as many as N=200N=200 sites, revealing the emergence of spatially-modulated magnetic order far from equilibrium. This approach offers promising prospects for advancing our understanding of the complex non-equilibrium properties of a diverse variety of experimentally-realizable quantum systems with long-ranged interactions, including Rydberg atoms, ultracold dipolar molecules, and trapped ions.

Block-Encoding Tensor Networks and QUBO Embeddings

Authors: Sebastian Issel

arXiv ID: 2510.00935 | Date: 2025-10-01

Abstract: We give an algorithm that converts any tensor network (TN) into a sequence of local unitaries whose composition block-encodes the network contraction, suitable for Quantum Eigenvalue / Singularvalue Transformation (QET/QSVT). The construction embeds each TN as a local isometry and dilates it to a unitary. Performing this step for every site of the tensor, allows the full network to be block-encoded. The theory is agnostic to virtual-bond sizes; for qubit resource counts and examples we assume global power-of-two padding. Further, we present a deterministic sweep that maps Quadratic Unconstrained Binary Optimization (QUBO) / Ising Hamiltonians into Matrix Product Operators (MPOs) and general TN. We provide formal statements, pseudo-code, resource formulae, and a discussion of the use for state preparation and learning of general quantum operators.

Efficient Probabilistic Tensor Networks

Authors: Marawan Gamal Abdel Hameed, Guillaume Rabusseau

arXiv ID: 2510.00382 | Date: 2025-10-01

Abstract: Tensor networks (TNs) enable compact representations of large tensors through shared parameters. Their use in probabilistic modeling is particularly appealing, as probabilistic tensor networks (PTNs) allow for tractable computation of marginals. However, existing approaches for learning parameters of PTNs are either computationally demanding and not fully compatible with automatic differentiation frameworks, or numerically unstable. In this work, we propose a conceptually simple approach for learning PTNs efficiently, that is numerically stable. We show our method provides significant improvements in time and space complexity, achieving 10x reduction in latency for generative modeling on the MNIST dataset. Furthermore, our approach enables learning of distributions with 10x more variables than previous approaches when applied to a variety of density estimation benchmarks. Our code is publicly available at github.com/marawangamal/ptn.

Dimerization in the SU(4) Heisenberg model on the cubic lattice: iPEPS study

Authors: Illia Lukin, Andrii Sotnikov

arXiv ID: 2510.00284 | Date: 2025-09-30

Abstract: We study SU(4)-symmetric Heisenberg model on the cubic lattice with spatially anisotropic magnetic couplings. We utilize several approaches based on the tensor-network representation of the many-body wave functions, which enable accurate analysis of ground-state properties of the model in different regimes of spatial anisotropy including fully isotropic three-dimensional case. Our results point to the persistence of the dimerized color-ordered phase throughout whole range of magnetic couplings excluding only the limit of completely decoupled one-dimensional chains.

Advantage of utilizing nonlocal magic resource in Haar-random circuits

Authors: Xiao Huang, Guanhua Chen, Yao Yao

arXiv ID: 2509.26342 | Date: 2025-09-30

Abstract: Magic resources and entanglement are fundamental components for achieving the universal quantum computation, so is the interplay between them. Herein, we uncover an intrinsic scaling law of the magic resource and bond dimension of matrix product states in Haar-random quantum circuits, that is, the magic resource is converged on a bond dimension in logarithmic scale with the system size. From a practical perspective, this finding substantially enhances the classical simulability of nonstabilizerness. It also allows us to utilize the bond dimension as a bridge to link the entanglement and the nonlocal magic resource, which extends the capacity perspective that the entanglement plays the role of container for the nonlocal magic resource. Furthermore, the intrinsic scaling enables an information separation between the nonlocal magic resource and the extra entanglement. This, in turn, leads to the conclusion that, any dynamical relation between magic and entanglement resources is ruled out. In other words, it is inappropriate to regard the entanglement as the driving force of the growth and spreading of nonlocal magic resource.

Why is topology hard to learn?

Authors: D. O. Oriekhov, Stan Bergkamp, Guliuxin Jin, Juan Daniel Torres Luna, Badr Zouggari, Sibren van der Meer, Naoual El Yazidi, Eliska Greplova

arXiv ID: 2509.26261 | Date: 2025-09-30

Abstract: Much attention has been devoted to the use of machine learning to approximate physical concepts. Yet, due to challenges in interpretability of machine learning techniques, the question of what physics machine learning models are able to learn remains open. Here we bridge the concept a physical quantity and its machine learning approximation in the context of the original application of neural networks in physics: topological phase classification. We construct a hybrid tensor-neural network object that exactly expresses real space topological invariant and rigorously assess its trainability and generalization. Specifically, we benchmark the accuracy and trainability of a tensor-neural network to multiple types of neural networks, thus exemplifying the differences in trainability and representational power. Our work highlights the challenges in learning topological invariants and constitutes a stepping stone towards more accurate and better generalizable machine learning representations in condensed matter physics.

Anderson localization: a density matrix approach

Authors: Ziyue Qi, Yi Zhang, Mingpu Qin, Hongming Weng, Kun Jiang

arXiv ID: 2509.26206 | Date: 2025-09-30

Abstract: Anderson localization is a quantum phenomenon in which disorder localizes electronic wavefunctions. In this work, we propose a new approach to study Anderson localization based on the density matrix formalism. Drawing an analogy to the standard transfer matrix method, we extract the localization length from the modular density matrix in quasi-one-dimensional systems. This approach successfully captures the metal-insulator transition in the three-dimensional Anderson model and in the two-dimensional Anderson model with spin-orbit coupling. It can be also readily extended to multiorbital systems. We further generalize the formalism to interacting systems, showing that the one-dimensional spinless attractive model exhibits the expected metallic phase, consistent with previous studies. More importantly, we demonstrate the existence of a two-dimensional metallic phase in the presence of Hubbard interactions and disorder. This method offers a new perspective on Anderson localization and its interplay with interactions.

Unsupervised Detection of Topological Phase Transitions with a Quantum Reservoir

Authors: Li Xin, Da Zhang, Zhang-Qi Yin

arXiv ID: 2509.25825 | Date: 2025-09-30

Abstract: In quantum many-body systems, characterizing topological phase transitions typically requires complex many-body topological invariants, which are costly to compute and measure. Inspired by quantum reservoir computing, we propose an unsupervised quantum phase detection method based on a many-body localized evolution, enabling efficient identification of phase transitions in the extended SSH model. The evolved quantum states produce feature distributions under local measurements, which, after simple post-processing and dimensionality reduction, naturally cluster according to different Hamiltonian parameters. Numerical simulations show that the evolution combined with local measurements can significantly amplify distinctions between quantum states, providing an efficient means to detect topological phase transitions. Our approach requires neither complex measurements nor full density matrix reconstruction, making it practical and feasible for noisy intermediate-scale quantum devices.

Origin of Spin Stripes in Bilayer Nickelate La3_3Ni2_2O7_7

Authors: Hao-Xin Wang, Hanbit Oh, Tobias Helbig, Bai Yang Wang, Jiarui Li, Yijun Yu, Harold Y. Hwang, Hong-Chen Jiang, Yi-Ming Wu, S. Raghu

arXiv ID: 2509.25344 | Date: 2025-09-29

Abstract: The bilayer nickelate La3_3Ni2_2O7_7 has emerged as a new high temperature superconductor. We propose and study a microscopic Hamiltonian that addresses the interplay of lattice structure and magnetism in this system. Using state-of-the-art density matrix renormalization group calculations, we show that (π/2,π/2)(π/2,π/2) spin stripe order emerges in our model and exhibits a hidden quasi-one dimensionality. The spin stripe order occurs over a range of electron concentrations, but requires a sizable Hund's coupling JHJ_H. Our model exhibits superconducting tendency only when the interlayer antiferromagnetic coupling JJ_\bot becomes sufficiently large, which naturally occurs under pressure. Our study unveils the microscopic origin of both the unusual spin stripes and superconductivity in La3_3Ni2_2O7_7, and highlights the indispensable role of Hund's coupling JHJ_H in this system.

Coupling induced emergent topology in a two-leg fermionic ladder

Authors: Rajashri Parida, Biswajit Paul, Soumya Ranjan Padhi, Tapan Mishra

arXiv ID: 2509.25130 | Date: 2025-09-29

Abstract: We investigate the ground state properties of spinless fermions on a two leg ladder, by allowing the nearest-neighbour hopping dimerization in one leg and uniform hopping in the other. In the non-interacting limit, we find that, at half-filling, the system exhibits robust topological behavior if the inter-leg hopping is allowed. Though depending on the dimerization pattern, the dimerized leg can be either topological or trivial in nature, here we show that by connecting such a leg to a uniform leg through inter-chain coupling, the overall system becomes topological irrespective of the dimerization pattern in the dimerized leg. As a result, a topological phase transition occurs as a function of the inter-leg hopping. When the inter-leg interaction is turned on, the topological phase survives, and we obtain an interaction induced topological phase transition. Finally, we reveal that when uniform interactions are included on all the bonds of the ladder, the topological phase transitions to a symmetry-broken charge-density wave (CDW) phase.

Strong enhancement of d-wave superconductivity in an extended checkerboard Hubbard ladder

Authors: Xichen Huang, Saisai He, Jize Zhao, Zhong-Bing Huang

arXiv ID: 2509.24415 | Date: 2025-09-29

Abstract: By employing the density-matrix renormalization group method, we study an extended checkerboard Hubbard model on the two-leg ladder, which includes an intraplaquette nearest-neighbour attraction V. The simulated results show that V plays a significant role in enhancing the d-wave superconductivity when the electron density is close to half-filling. In the homogeneous case t'=t (t and t' are the intraplaquette and interplaquette hopping integrals), large critical |Vc| is required to induce the superconducting ground state. With decreasing t', |Vc| is substantially diminished and the pair state has a nearly C4 symmetry. In the extremely inhomogeneous case t'<0.2t, the system transits to the d-wave superconducting phase at V\sim-0.3t and V\sim-0.4t for U=8t and U=12t, respectively, accompanying with a shift of spin and single-particle excitations from gapless to gapped type.

Tensor Network Markov Chain Monte Carlo: Efficient Sampling of Three-Dimensional Spin Glasses and Beyond

Authors: Tao Chen, Jing Liu, Youjin Deng, Pan Zhang

arXiv ID: 2509.23945 | Date: 2025-09-28

Abstract: Sampling the three-dimensional (3D) spin glass -- i.e., generating equilibrium configurations of a 3D lattice with quenched random couplings -- is widely regarded as one of the central and long-standing open problems in statistical physics. The rugged energy landscape, pronounced critical slowing down, and intrinsic ergodicity breaking render standard Monte Carlo methods severely inefficient, particularly for large systems at low temperatures. In this work, we introduce the Tensor Network Markov Chain Monte Carlo (TNMCMC) approach to address the issue. It generates large-scale collective updates in MCMC using tensor networks on the 2D slices of the 3D lattice, greatly improving the autocorrelation time and offering orders-of-magnitude speed-ups over conventional MCMC in generating unbiased samples of the Boltzmann distribution. We conduct numerical experiments on 3D spin glasses up to system size 64×64×6464\times 64\times 64 using a single CPU, and show that TNMCMC dramatically suppresses critical slowing down in large disordered systems, which usually require a supercomputer to perform MCMC simulations. Furthermore, we apply our approach to the 3-state Potts model up to system size 64×64×6464\times 64\times 64 using a single CPU, and show that the TNMCMC approach efficiently traverses the exponential barriers of the strong first-order transition, whereas conventional MCMC fails. Our results reveal that TNMCMC opens a promising path toward tackling long-standing, formidable three-dimensional problems in statistical physics.

Power-Law Spectra and Asymptotic ω/Tω/T Scaling in the Orbital-Selective Mott Phase of a Three-Orbital Hubbard Model

Authors: Fabian Eickhoff

arXiv ID: 2509.23758 | Date: 2025-09-28

Abstract: Quantum materials whose properties lie beyond the celebrated Landau Fermi-liquid paradigm have been observed for decades across diverse material platforms. Finding microscopic lattice models for metallic states that exhibit such peculiar behavior remains a major theoretical challenge, as these features often originate from strong quantum fluctuations in strongly interacting electron systems. Here we investigate a three-orbital Hubbard model at a high-symmetry point that hosts a transition from a metallic to an orbital-selective Mott (OSM) phase. Employing single-site dynamical mean-field theory combined with full-density-matrix numerical renormalization group, we chart the TUT-U phase diagram and obtain high-resolution real-frequency dynamics. In the OSM regime we find asymptotically scale-invariant (power-law) single-particle spectra and asymptotic ω/Tω/T scaling in both charge and spin channels, spanning several decades in frequency and temperature.

Haag Duality for 2D Quantum Spin Systems

Authors: Yoshiko Ogata, David Pérez-García, Alberto Ruiz-de-Alarcón

arXiv ID: 2509.23734 | Date: 2025-09-28

Abstract: Haag duality is a fundamental locality property introduced in the pioneering formulation of algebraic quantum field theory by Haag and Kastler in the 1960s. Since then, it has played a central role, most notably in the classification of superselection sectors by Doplicher, Haag, and Roberts in the 1970s. Over the past two decades, this concept has migrated from its relativistic origins to quantum spin systems, becoming a cornerstone of the operator-algebraic approach to the long-standing problem of classifying two-dimensional topological quantum phases of matter. In physics, it is widely conjectured that such phases are classified by their emergent anyons, a view supported by exactly solvable models exemplifying all known non-chiral phases: Kitaev's quantum double models, Levin-Wen string-net models, and their slight generalizations. In these models, elementary excitations behave as quasi-particles, namely anyons, whose fusion and braiding properties form a tensor category expected to characterize the phase of matter. A major open problem was to derive the emergence of anyons and the stability of their fusion and braiding beyond these solvable models. Recently, it has been shown that a weaker, phase-stable form of Haag duality resolves these questions. However, rigorous proofs of Haag duality in two dimensions were previously restricted to systems exhibiting abelian anyons. In this work, we establish Haag duality for a broad class of tensor network models based on CC^*-weak Hopf algebras, encompassing all Kitaev quantum double and Levin-Wen string-net models, and expected to include all non-chiral topological quantum phases of matter.

Phase structure of (3+1)-dimensional dense two-color QCD at T=0T=0 in the strong coupling limit with tensor renormalization group

Authors: Yuto Sugimoto, Shinichiro Akiyama, Yoshinobu Kuramashi

arXiv ID: 2509.23637 | Date: 2025-09-28

Abstract: We investigate the phase structure of the (3+1)-dimensional strong coupling two-color QCD at zero temperature with finite chemical potential using the tensor renormalization group method. The chiral and diquark condensates and the quark number density are evaluated as a function of the chemical potential. Our results are compared with the previous analytical results using the mean field approximation. The critical exponents associated with the diquark condensation are also discussed.

Exploring Magnetic Phases in Dual-Species Mott insulating Spinor Lattice Gases

Authors: Rui-Shan Li, Zong-Zhen Pan, Shi-Jie Yang, Yi Zheng

arXiv ID: 2509.23142 | Date: 2025-09-27

Abstract: We explore the Mott insulating phases of dual-species bosonic spinor lattice gases, emphasizing the intriguing interplay between synthetic flux and inter-species spin exchange interaction. One of the species is subjected to Raman assisted tunneling, which leads to a synthetic flux within the framework of synthetic dimensions. In the deep Mott regime, the low energy physics is governed by an unconventional and highly tunable spin model, which is characterized by two distinct spin chains. The synthetic flux serves as an effective spin-orbit coupling, inducing Dzyaloshinskii-Moriya interactions in one of the spin chains. The inter-species spin exchange interaction gives rise to the inter-chain coupling embodied as an isotropic XX interaction. Using time-evolving block decimation method for tensor network states, we compute order parameters, correlation functions and structure factors to identify the ground state magnetic phases. The DM interaction in one species, when combined with the inter-species spin-exchange interaction, can induce spiral magnetic order in the second, otherwise non-chiral species. Besides, the interplay of a transverse field applied to one spin chain and the inter-species coupling can drive both spin chains into a paramagnetic phase simultaneously. These results reveal that inter-species coupling serves as a powerful conduit for transmitting magnetic correlations, enabling exotic phases beyond the single-component perspective.

Entanglement and apparent thermality in simulated black holes

Authors: Iason A. Sofos, Andrew Hallam, Jiannis K. Pachos

arXiv ID: 2509.22774 | Date: 2025-09-26

Abstract: We investigate the apparent thermality of Hawking radiation in the semi-classical limit of quantum black holes using the mean-field limit of a chiral spin-chain simulator, which models fermions propagating on a black hole space-time in the continuum. In this free-theory regime, no genuine thermalisation occurs. Nevertheless, we show that a bipartition across the event horizon yields a reduced density matrix whose mode occupations follow an apparent thermal Fermi-Dirac distribution. In contrast, partitions away from the horizon do not exhibit thermal behaviour, reflecting the absence of true equilibration. Our results demonstrate that Hawking radiation appears thermal only with respect to horizon bipartitions in free theories, while true thermal behaviour emerges only in the presence of interactions deep in the black hole interior.

Universality of Shallow Global Quenches in Critical Spin Chains

Authors: Julia Wei, Méabh Allen, Jack Kemp, Chenbing Wang, Zixia Wei, Joel E. Moore, Norman Y. Yao

arXiv ID: 2509.22773 | Date: 2025-09-26

Abstract: Measuring universal data in the strongly correlated regime of quantum critical points remains a fundamental objective for quantum simulators. In foundational work, Calabrese and Cardy demonstrated how this data governs the dynamics of certain global quenches to 1+1-dimensional conformal field theories. While the quasiparticle picture they introduce has been widely successful in both theory and experiment, their seminal prediction that the critical exponents are simply encoded in the relaxation rates of local observables is more challenging to investigate experimentally; in particular, the specific initial state required for their analysis is generated via imaginary time evolution. In this work, we examine the critical quench dynamics of local observables from two types of readily-accessible initial conditions: ground states and finite-temperature ensembles. We identify universal scaling collapses and scaling functions in both cases, utilizing a combination of conformal perturbation theory and tensor network numerics. For the finite-temperature quenches, we determine a regime in which the conformal field theory results are recovered, thereby allowing universal quantum critical data to be extracted from realistic quenches.

Competing ss-wave pairing in overdoped tt-JJ model

Authors: Wayne Zheng, Tao Cheng, Zheng-Yuan Yue, Fu-Chun Zhang, Wei-Qiang Chen, Zheng-Cheng Gu

arXiv ID: 2509.22473 | Date: 2025-09-26

Abstract: The dd-wave pairing symmetry has long been considered a defining feature of high-temperature superconductivity in cuprates. In this work, we reveal that ss-wave pairing states exhibit variational energies comparable to the dd-wave state in a square tt-JJ model, particularly at high doping levels (δ15%δ\gtrsim 15\%) by using the state-of-the-art tensor network simulation. This surprising result suggests that ss-wave pairing may play an important role in the cuprate phase diagram, especially for the overdoped region. Our findings provide a potential resolution to discrepancies in recent Josephson tunneling experiments on twisted bilayer cuprates and offer new insights into the evolution of pairing symmetry with doping.

Tubular partitions and representations of the quantum automorphism group of a homogeneous rooted tree

Authors: Nathan Brownlowe, David Robertson

arXiv ID: 2509.22201 | Date: 2025-09-26

Abstract: We introduce the rigid tensor category of tubular partitions, and use it to provide a combinatorial model for the representation category of the quantum automorphism group of a homogeneous rooted tree.

Kernel Regression of Multi-Way Data via Tensor Trains with Hadamard Overparametrization: The Dynamic Graph Flow Case

Authors: Duc Thien Nguyen, Konstantinos Slavakis, Eleftherios Kofidis, Dimitris Pados

arXiv ID: 2509.22197 | Date: 2025-09-26

Abstract: A regression-based framework for interpretable multi-way data imputation, termed Kernel Regression via Tensor Trains with Hadamard overparametrization (KReTTaH), is introduced. KReTTaH adopts a nonparametric formulation by casting imputation as regression via reproducing kernel Hilbert spaces. Parameter efficiency is achieved through tensors of fixed tensor-train (TT) rank, which reside on low-dimensional Riemannian manifolds, and is further enhanced via Hadamard overparametrization, which promotes sparsity within the TT parameter space. Learning is accomplished by solving a smooth inverse problem posed on the Riemannian manifold of fixed TT-rank tensors. As a representative application, the estimation of dynamic graph flows is considered. In this setting, KReTTaH exhibits flexibility by seamlessly incorporating graph-based (topological) priors via its inverse problem formulation. Numerical tests on real-world graph datasets demonstrate that KReTTaH consistently outperforms state-of-the-art alternatives-including a nonparametric tensor- and a neural-network-based methods-for imputing missing, time-varying edge flows.

Predictor-corrector method based on dynamic mode decomposition for tensor-train nonequilibrium Green's function calculations

Authors: Maksymilian Środa, Ken Inayoshi, Michael Schüler, Hiroshi Shinaoka, Philipp Werner

arXiv ID: 2509.22177 | Date: 2025-09-26

Abstract: The nonequilibrium Green's function (NEGF) formalism is a powerful tool to study the nonequilibrium dynamics of correlated lattice systems, but its applicability to realistic system sizes and long timescales is limited by unfavorable memory scaling. While compressed representations, such as the recently introduced quantics tensor train (QTT) format, alleviate the memory bottleneck, the efficiency of QTT-NEGF calculations is hindered by poor initializations and slow or unstable convergence of globally updated self-consistent iterations. Here, we introduce a predictor-corrector solver for QTT-NEGF simulations that combines dynamic mode decomposition (DMD) extrapolation with the recently proposed causality-preserving block-time-stepping updates. The DMD predictor supplies accurate initial guesses that reduce the iteration count of the calculation, while the block-time-stepping correction ensures stable convergence even for long propagation intervals. Applying this method to the Hubbard model on a 32×3232\times 32 lattice within the nonequilibrium GWGW approximation, we demonstrate stable propagation up to times of tmax=512t_\mathrm{max}=512 inverse hoppings, surpassing the capabilities of both matrix-based implementations and previous QTT solvers. Our contribution is twofold. (i) We integrate tensor dynamic mode decomposition with the QTT representation, which establishes a general framework that is not limited to NEGFs. (ii) We demonstrate its practical benefits in NEGF simulations, where it enables stable and efficient access to unprecedented timescales at high momentum resolution, thereby advancing controlled studies of long-time dynamics and nonequilibrium steady states in correlated lattice systems.

Introduction to modelling radical pair quantum spin dynamics with tensor networks

Authors: Kentaro Hino, Damyan S. Frantzov, Yuki Kurashige, Lewis M. Antill

arXiv ID: 2509.22104 | Date: 2025-09-26

Abstract: Radical pairs (also known as spin qubit pairs, electron-hole pairs) are transient reaction intermediates that are found and utilised in all areas of science. Radical pair spin dynamics simulations including all nuclear spins have been a computational barrier due to exponential scaling memory requirements. We address this issue with a tensor network method for accurately simulating the full open quantum dynamics of radical pair systems, explicitly accounting for hyperfine interactions with up to 30 nuclear spins with additional benchmarking including 60 nuclei. By employing the matrix product state (MPS) and matrix product density operator (MPDO) representations, we mitigate the exponential scaling of Hilbert and Liouville spaces typically encountered in full quantum non-Markovian treatments. We demonstrate the power of these methods with biologically relevant flavin-tryptophan radical pair systems, where we investigate electron hopping processes between multiple radical pairs using Lindblad jump operators. These simulations precisely capture anisotropic spin dynamics, clearly identifying orientational dependence of the magnetic field, which enhances or diminishes the spin-selective product yield. These directional sensitivities highlight the critical dependence of the nuclear environment and underscore the necessity of fully quantum treatments in spin biophysics, offering critical insights into avian magnetoreception mechanisms. This work provides a robust computational framework applicable to a broad range of scientific realms, which include spin chemistry, quantum biology, and spintronics.

From gauging to duality in one-dimensional quantum lattice models

Authors: Bram Vancraeynest-De Cuiper, José Garre-Rubio, Frank Verstraete, Kevin Vervoort, Dominic J. Williamson, Laurens Lootens

arXiv ID: 2509.22051 | Date: 2025-09-26

Abstract: Gauging and duality transformations, two of the most useful tools in many-body physics, are shown to be equivalent up to constant depth quantum circuits in the case of one-dimensional quantum lattice models. This is demonstrated by making use of matrix product operators, which provide the lattice representation theory for global (categorical) symmetries as well as a classification of duality transformations. Our construction makes the symmetries of the gauged theory manifest and clarifies how to deal with static background fields when gauging generalised symmetries.

Gapless and ordered phases in spin-1/2 Kitaev-XX-Gamma chain

Authors: Zebin Zhuang, Wang Yang

arXiv ID: 2509.21901 | Date: 2025-09-26

Abstract: In this work, we study the spin-1/2 Kitaev chain with additional XX and symmetric off-diagonal Gamma interactions. By a combination of Jordan-Wigner transformation and density matrix renormalization group (DMRG) numerical simulations, we obtain the exact solution of the model and map out the phase diagram containing six distinct phases. The four gapped phases display ferromagnetic and antiferromagnetic magnetic orders along the (1, 1, 0)- and (1, -1, 0)-spin directions, whereas in the gapless phases, the low energy spectrum consists of two branches of helical Majorana fermions with unequal velocities. Transition lines separating different phases include deconfined quantum critical lines with dynamical critical exponent z = 1 and quadratic critical lines with z = 2. Our work reveals the rich interplay among symmetry, magnetic order, and quantum criticality in the Kitaev-XX-Gamma chain

Low-energy photoexcitation inside the Mott gap in doped Hubbard and t-J ladders

Authors: Sumal Chandra, Kazuya Shinjo, Shigetoshi Sota, Seiji Yunoki, Takami Tohyama

arXiv ID: 2509.21813 | Date: 2025-09-26

Abstract: We investigate changes in the optical conductivity of doped Mott insulators by tuning ultrashort pump pulses to target either the Drude or low-energy absorption regions. Using a hole-doped two-leg Hubbard ladder and a four-leg t-J ladders, we calculate the optical conductivity after pump by employing the time-dependent density matrix renormalization group. We find that a monocycle electric field pulse tuned to the Drude absorption reduces the Drude weight, accompanied by a slight enhancement in the mid-infrared (mid-IR) spectral weight. However, this enhancement diminishes as the pulse intensity increases. In contrast, a pump pulse tuned to the mid-IR absorption only affects the Drude weight. This behavior arises because the mid-IR absorption originates from magnetic excitations that do not couple directly to photons. These predictions can be tested experimentally by applying ultrashort low-energy pump pulses to cuprate materials.

DisCoCLIP: A Distributional Compositional Tensor Network Encoder for Vision-Language Understanding

Authors: Kin Ian Lo, Hala Hawashin, Mina Abbaszadeh, Tilen Limback-Stokin, Hadi Wazni, Mehrnoosh Sadrzadeh

arXiv ID: 2509.21287 | Date: 2025-09-25

Abstract: Recent vision-language models excel at large-scale image-text alignment but often neglect the compositional structure of language, leading to failures on tasks that hinge on word order and predicate-argument structure. We introduce DisCoCLIP, a multimodal encoder that combines a frozen CLIP vision transformer with a novel tensor network text encoder that explicitly encodes syntactic structure. Sentences are parsed with a Combinatory Categorial Grammar parser to yield distributional word tensors whose contractions mirror the sentence's grammatical derivation. To keep the model efficient, high-order tensors are factorized with tensor decompositions, reducing parameter count from tens of millions to under one million. Trained end-to-end with a self-supervised contrastive loss, DisCoCLIP markedly improves sensitivity to verb semantics and word order: it raises CLIP's SVO-Probes verb accuracy from 77.6% to 82.4%, boosts ARO attribution and relation scores by over 9% and 4%, and achieves 93.7% on a newly introduced SVO-Swap benchmark. These results demonstrate that embedding explicit linguistic structure via tensor networks yields interpretable, parameter-efficient representations that substantially improve compositional reasoning in vision-language tasks.

Anomalous Quantum Relaxation in the Infinite Temperature Hubbard Chain

Authors: Catalin Pascu Moca, Balázs Dóra

arXiv ID: 2509.20759 | Date: 2025-09-25

Abstract: The self-energy encodes the fundamental lifetime of quasiparticle excitations. In one dimension, it is known to display anomalous behavior at zero temperature for interacting fermions, reflecting the breakdown of Fermi-liquid theory. Here we show that the self-energy is also anomalous in the infinite temperature Hubbard chain, where thermal fluctuations are maximal. Focusing on the second order ring diagram, we find that the imaginary part of the self-energy diverges non-perturbatively: as a power law with exponent 1/3-1/3 near half filling, and logarithmically away from it. These divergences imply anomalous temporal relaxation of Green's functions, confirmed by infinite temperature tensor-network simulations. Our results demonstrate that anomalous relaxation and the breakdown of perturbation theory survive even at maximal entropy, which can be observed in cold-atom experiments probing the Hubbard chain at high temperatures.

Numerically exact quantum dynamics with tensor networks: Predicting the decoherence of interacting spin systems

Authors: Tianchu Li, Pranay Venkatesh, Nanako Shitara, Andrés Montoya-Castillo

arXiv ID: 2509.20604 | Date: 2025-09-24

Abstract: Predicting the quantum dynamics of promising solid-state and molecular quantum technology candidates remains a formidable challenge. Yet, accessing these dynamics is key to understanding and controlling decoherence mechanisms -- a prerequisite for designing better qubits, sensors, and memories. We leverage a matrix product state representation to introduce a numerically exact and scalable method to achieve this goal. We demonstrate that our method accurately predicts coherence and population dynamics of spin networks across a wide range of parameter regimes, encompassing nuclear spin sensors and qubits in solid-state semiconductors and molecular magnets. Our method further predicts spin dynamics under the influence of repeated light pulses, which are commonly used to mitigate decoherence and perform quantum sensing experiments. Our method thus provides reliable results for moderately-sized spin platforms spanning molecular magnets and solid-state spins that can guide the development of approximate but efficient quantum dynamics methods and enable principled inquiry into decoherence mechanisms.

Quantum Coherence in a Maximally Hot Hubbard Chain

Authors: Cătălin Paşcu Moca, Ovidiu I. Patu, Balázs Dóra, Gergely Zaránd

arXiv ID: 2509.20498 | Date: 2025-09-24

Abstract: We present a detailed study of the real-time dynamics and spectral properties of the one-dimensional fermionic Hubbard model at infinite temperature. Using tensor network simulations in Liouville space, we compute the single-particle Green's function and analyze its dynamics across a broad range of interaction strengths. To complement the time-domain approach, we develop a high-resolution Chebyshev expansion method within the density matrix formalism, enabling direct access to spectral functions in the frequency domain. In the non-interacting limit, we derive exact analytical expressions for the Green's function, providing a benchmark for our numerical methods. As interactions are introduced, we observe a transition in the spectral function from a sharp peak at the free dispersion to a broadened two-band structure associated with hole and doublon excitations. These features are well captured by a Hubbard-I mean-field approximation, even at intermediate coupling. At infinite interaction strength (U=U = \infty), we exploit a determinant representation of the Green's function to access both real-time and spectral properties. In this regime, the system retains a sharp, cosine-like momentum dispersion in frequency space, while the dynamics display nontrivial light-cone spreading with sub-ballistic scaling. Our results demonstrate that strong correlations and nontrivial quantum coherence can persist even at infinite temperature.

Multicriticality between Purely Gapless SPT Phases with Unitary Symmetry

Authors: Saranesh Prembabu, Ruben Verresen

arXiv ID: 2509.20431 | Date: 2025-09-24

Abstract: Symmetry-protected topological (SPT) phases are commonly required to have an energy gap, but recent work has extended the concept to gapless settings. This raises a natural question: what happens at transitions between inequivalent gapless SPTs? We address this for the simplest known case among gapless SPTs protected by a unitary symmetry group acting faithfully on the low-energy theory. To this end, we consider a qutrit version of the nearest-neighbor XX chain. Trimerizing the chain explicitly breaks an anomalous symmetry and produces three distinct gapped SPT phases protected by a unitary Z3×Z3\mathbb{Z}_3 \times \mathbb{Z}_3 symmetry. Their phase boundaries are given by three inequivalent gapless SPTs without any gapped symmetry sectors, each described by a symmetry-enriched version of an orbifolded Potts2^2 conformal field theory with central charge c=85c=\frac{8}{5}. We provide an analytic derivation of this critical theory in a particular regime and confirm its stability using tensor network simulations. Remarkably, the three gapless SPTs meet at a c=2c = 2 multicritical point, where the protecting Z3×Z3\mathbb{Z}_3 \times \mathbb{Z}_3 symmetry exhibits a mixed anomaly with the Z3\mathbb Z_3 entangler symmetry that permutes the SPT classes. We further explore how discrete gauging gives dipole-symmetric models, offering insights into dipole symmetry-breaking and SPTs, as well as symmetry-enriched multiversality. Altogether, this work uncovers a rich phase diagram of a minimal qutrit chain, whose purely nearest-neighbor interactions make it a promising candidate for experimental realization, including the prospect of critical phases with stable edge modes.

Computational complexity of injective projected entangled pair states

Authors: Dylan Harley, Freek Witteveen, Daniel Malz

arXiv ID: 2509.19963 | Date: 2025-09-24

Abstract: Projected entangled pair states (PEPS) constitute a variational family of quantum states with area-law entanglement. PEPS are particularly relevant and successful for studying ground states of spatially local Hamiltonians. However, computing local expectation values in these states is known to be \postBQP-hard. Injective PEPS, where all constituent tensors fulfil an injectivity constraint, are generally believed to be better behaved, because they are unique ground states of spatially local Hamiltonians. In this work, we therefore examine how the computational hardness of contraction depends on the injectivity. We establish that below a constant positive injectivity threshold, evaluating local observables remains \postBQP-complete, while above a different constant nontrivial threshold there exists an efficient classical algorithm for the task, resolving an open question from (Anshu et al., STOC `24). We do this by proving that noisy postselected quantum computation can be made fault-tolerant.

Automatic Structure Identification for Highly Nonlinear MIMO Volterra Tensor Networks

Authors: Eva Memmel, Kim Batselier

arXiv ID: 2509.19627 | Date: 2025-09-23

Abstract: The Volterra Tensor Network lifts the curse of dimensionality for truncated, discrete times Volterra models, enabling scalable representation of highly nonlinear system. This scalability comes at the cost of introducing randomness through initialization, and leaves open the challenge of how to efficiently determine the hyperparameters model order and memory length. In this paper, we present a unified framework that simultaneously addresses both challenges: We derive two algorithms that incrementally increase the model order and memory length along. Further we proof that the updates are performed along conjugate directions by establishing a mathematical equivalence between our proposed algorithms and equality constrained least squares systems. We present several strategies how to use our proposed algorithms for initialization and hyperparameter selection. In numerical experiments, we demonstrate that our proposed algorithms are more accurate and efficient than the state-of-the-art Volterra Tensor Network and achieve competitive results to several state-of-the-art Volterra models.

Regularity estimate and sparse approximation of pathwise robust Duncan-Mortensen-Zakai equation

Authors: Yuhua Meng, Zhongjian Wang, Stephen S. T. Yau, Zhiwen Zhang

arXiv ID: 2509.19093 | Date: 2025-09-23

Abstract: In this paper, we establish an \textit{a priori} estimate for arbitrary-order derivatives of the solution to the pathwise robust Duncan-Mortensen-Zakai (DMZ) equation within the framework of weighted Sobolev spaces. The weight function, which vanishes on the physical boundary, is crucial for the \textit{a priori} estimate, but introduces a loss of regularity near the boundary. Therefore, we employ the Sobolev inequalities and their weighted analogues to sharpen the regularity bound, providing improvements in both classical Sobolev spaces and H{ö}lder continuity estimates. The refined regularity estimate reinforces the plausibility of the quantized tensor train (QTT) method in [S. Li, Z. Wang, S. S.-T. Yau, and Z. Zhang, IEEE Trans. Automat. Control, 68 (2023), pp. 4405--4412] and provides convergence guarantees of the method. To further enhance the capacity of the method to solve the nonlinear filtering problem in a real-time manner, we reduce the complexity of the method under the assumption of a functional polyadic state drift ff and observation hh. Finally, we perform numerical simulations to reaffirm our theory. For high-dimensional cubic sensor problems, our method demonstrates superior efficiency and accuracy in comparison to the particle filter (PF) and the extended Kalman filter (EKF). Beyond this, for multi-mode problems, while the PF exhibits a lack of precision due to its stochastic nature and the EKF is constrained by its Gaussian assumption, the enhanced method provides an accurate reconstruction of the multi-mode conditional density function.

BatchTNMC: Efficient sampling of two-dimensional spin glasses using tensor network Monte Carlo

Authors: Tao Chen, Jingtong Zhang, Jing Liu, Youjin Deng, Pan Zhang

arXiv ID: 2509.19006 | Date: 2025-09-23

Abstract: Efficient sampling of two-dimensional statistical physics systems remains a central challenge in computational statistical physics. Traditional Markov chain Monte Carlo (MCMC) methods, including cluster algorithms, provide only partial solutions, as their efficiency collapses for large systems in the presence of frustration and quenched disorder. The recently proposed Tensor Network Monte Carlo (TNMC) method offers a promising alternative, yet its original implementation suffers from inefficiencies due to the lack of scalable parallel sampling. In this work, we introduce BatchTNMC, a GPU-optimized and parallelized implementation of TNMC tailored for large-scale simulations of two-dimensional spin glasses. By leveraging batch processing and parallel sampling across multiple disorder realizations, our implementation achieves speedups of up to five orders of magnitude compared with the original serial scheme. Benchmarking on two-dimensional spin glasses demonstrates dramatic gains in efficiency: for instance, on a single GPU, BatchTNMC concurrently produces 1000 uncorrelated and unbiased samples across 1000 disorder realizations on 1024×10241024\times 1024 lattices in just 3.3 hours, with an acceptance probability of 37%. These results establish BatchTNMC as a scalable and powerful computational framework for the study of two-dimensional disordered spin glass systems.

Order from chaos with adaptive circuits on quantum hardware

Authors: Bibek Pokharel, Haining Pan, Kemal Aziz, Luke C. G. Govia, Sriram Ganeshan, Thomas Iadecola, Justin H. Wilson, Barbara A. Jones, Abhinav Deshpande, Jedediah H. Pixley, Maika Takita

arXiv ID: 2509.18259 | Date: 2025-09-22

Abstract: Programmable quantum devices provide a platform to control the coherent dynamics of quantum wavefunctions. Here we experimentally realize adaptive monitored quantum circuits, which incorporate conditional feedback into non-unitary evolution, to control quantum chaotic dynamics using a combination of local mid-circuit measurements and resets. The experiments are performed with an IBM superconducting quantum processor using up to 100 qubits that samples a quantum version of the classically chaotic Bernoulli map. This map scrambles quantum information, while local measurements and feedback attempt to steer the dynamics toward a state that is a fixed point of the map. This competition drives a dynamical phase transition between quantum and classical dynamics that we observe experimentally and describe theoretically using noisy simulations, matrix product states, and mappings to statistical mechanics models. Estimates of the universal critical properties are obtained to high accuracy on the quantum computer thanks to the large number of qubits utilized in the calculation. By successfully applying up to nearly 5000 entangling gates and 5000 non-unitary mid-circuit operations on systems up to 100 qubits, this experiment serves as a signpost on the route towards fault tolerance.

Optimal local basis truncation of lattice quantum many-body systems

Authors: Peter Majcen, Giovanni Cataldi, Pietro Silvi, Simone Montangero

arXiv ID: 2509.17975 | Date: 2025-09-22

Abstract: We show how to optimally reduce the local Hilbert basis of lattice quantum many-body (QMB) Hamiltonians. The basis truncation exploits the most relevant eigenvalues of the estimated single-site reduced density matrix (RDM). It is accurate and numerically stable across different model phases, even close to quantum phase transitions. We apply this procedure to different models, such as the Sine-Gordon model, the φ4\varphi^{4} theory, and lattice gauge theories, namely Abelian U(1)\mathrm{U}(1) and non-Abelian SU(2)\mathrm{SU}(2), in one and two spatial dimensions. Our results reduce state-of-the-art estimates of computational resources for classical and quantum simulations.

Fast and Accurate Decoder for the XZZX code Using Simulated Annealing

Authors: Tatsuya Sakashita

arXiv ID: 2509.17837 | Date: 2025-09-22

Abstract: The XZZX code is a variant of the surface code designed to address biased noise in realistic quantum devices. For the XZZX code, we propose a decoder based on simulated annealing (SA). Our SA decoder can be readily and efficiently parallelized, by virtue of its simple MCMC-based algorithm. To prepare an initial configuration of SA, we propose to employ recovery chains obtained by a decoder which utilizes a kind of greedy matching graph algorithm. Although ZZ-biased noise is commonly assumed in real quantum devices, we focus on YY-biased noise, for which the minimum-weight perfect matching (MWPM) algorithm fails to decode accurately. Our numerical simulation for the code capacity noise model, where only data qubits suffer errors, confirmed that our SA decoder is more accurate than the MWPM decoder. Furthermore, our SA decoder attained the accuracy equivalent to that of the optimal decoder formulated by integer programming, called CPLEX decoder. In our greedy matching decoder, we randomly determine order of matching pairs of incorrect syndromes that have the same distance. This randomness brings about a variety of initial configurations of SA, which leads to faster convergence of our SA decoder. By comparing decoding times of our SA decoder, the CPLEX decoder, and matrix product state (MPS) decoder, all of which can handle YY-biased noise appropriately, we confirmed that our SA decoder is fastest if parallelized. This result implies a potential for combining of our greedy matching and SA decoder for practical use in quantum computing.

Noise robustness of problem-to-simulator mappings for quantum many-body physics

Authors: Rahul Trivedi, J. Ignacio Cirac

arXiv ID: 2509.17579 | Date: 2025-09-22

Abstract: Simulating quantum dynamics on digital or analog quantum simulators often requires ``problem-to-simulator" mappings such as trotterization, floquet-magnus expansion or perturbative expansions. When the simulator is noiseless, it is well understood that these problem-to-simulator mappings can be made as accurate as desired at the expense of simulator run-time. However, precisely because the simulator has to be run for a longer time to increase its accuracy, it is expected that noise in the quantum simulator catastrophically effects the simulator output. We show that, contrary to this expectation, these mappings remain stable to noise when considering the task of simulating dynamics of local observables in quantum lattice models. Specifically, we prove that in all of these mappings, local observables can be determined to a system-size independent, precision that scales sublinearly with the noise-rate in the simulator. Our results provide theoretical evidence that quantum simulators can be used for solving problems in many-body physics without or with modest error correction.

Universal Scaling Functions of the Gr{ü}neisen Ratio near Quantum Critical Points

Authors: Xuan Zhou, Enze Lv, Wei Li, Yang Qi

arXiv ID: 2509.17362 | Date: 2025-09-22

Abstract: The Grüneisen ratio, defined as Γg(1/T)(T/g)SΓ_g \equiv (1/T) (\partial T/\partial g)_S, serves as a highly sensitive probe for detecting quantum critical points (QCPs) driven by an external feild gg and for characterizing the magnetocaloric effect (MCE). Near a QCP, the Grüneisen ratio displays a universal divergence which is governed by a universality-class-dependent scaling function stemming from the scale invariance. In this work, we systematically investigate the universal scaling functions of Grüneisen ratio in both one-dimensional (1D) and two-dimensional (2D) quantum spin systems, including the transverse-field Ising model, the spin-1/2 Heisenberg model, the quantum qq-state Potts model (q=3,4q=3,4) and the J1J_1-J2J_2 columnar dimer model. Our approach employs the thermal tensor-network method for infinite-size 1D systems and the stochastic series expansion quantum Monte Carlo (SSE QMC) simulations for 2D systems, enabling precise calculations of the Grüneisen ratio near QCPs. Through data collapse analysis, we extract the corresponding scaling functions, which establish quantitative frameworks to interpret magnetocaloric experiments and guide the development of ultralow-temperature refrigeration.

Nonadiabatic H-Atom Scattering Channels on Ge(111) Elucidated by the Hierarchical Equations of Motion

Authors: Xiaohan Dan, Zhuoran Long, Tianyin Qiu, Jan Paul Menzel, Qiang Shi, Victor Batista

arXiv ID: 2509.16916 | Date: 2025-09-21

Abstract: Atomic and molecular scattering at semiconductor interfaces plays a central role in surface chemistry and catalysis, yet predictive simulations remain challenging due to strong nonadiabatic effects causing the breakdown of the Born-Oppenheimer approximation. Here, we present fully quantum simulations of H-atom scattering from the Ge(111)c(2x8) rest site using the hierarchical equations of motion (HEOM) with matrix product states (MPS). The system is modeled by mapping a density functional theory (DFT) potential energy surface onto a Newns-Anderson Hamiltonian. Our simulations reproduce the experimentally observed bimodal kinetic energy distributions, capturing both elastic and energy-loss channels. By systematically examining atom-surface coupling, incident energy, and isotope substitution, we identify the strong-coupling regime required to recover the experimental energy-loss profile. This regime suppresses the elastic peak, implying additional site-specific scattering channels in the observed elastic peak. Deuterium substitution further produces a subtle shift in the energy-loss peak, consistent with experiment. These results establish HEOM as a rigorous framework for quantum surface scattering, capable of capturing nonadiabatic dynamics beyond electronic friction and perturbative approaches.

Quantum State Tomography for Tensor Networks in Two Dimensions

Authors: Zhen Qin, Zhihui Zhu

arXiv ID: 2509.16852 | Date: 2025-09-21

Abstract: Recent work has shown that for one-dimensional quantum states that can be effectively approximated by matrix product operators (MPOs), a polynomial number of copies of the state suffices for reconstruction. Compared to MPOs in one dimension, projected entangled-pair states (PEPSs) and projected entangled-pair operators (PEPOs), which represent typical low-dimensional structures in two dimensions, are more prevalent as a looped tensor network. However, a formal analysis of the sample complexity required for estimating PEPS or PEPO has yet to be established. In this paper, we aim to address this gap by providing theoretical guarantees for the stable recovery of PEPS and PEPO. Our analysis primarily focuses on two quantum measurement schemes: (i)(i) informationally complete positive operator valued measures (IC-POVMs), specifically the spherical tt-designs (t3t \geq 3), and (ii)(ii) projective rank-one measurements, in particular Haar random projective measurements. We first establish stable embeddings for PEPSs (or PEPOs) to ensure that the information contained in the states can be preserved under these two measurement schemes. We then show that a constrained least-squares estimator achieves stable recovery for PEPSs (or PEPOs), with the recovery error bounded when the number of state copies scales linearly under spherical tt-designs and polynomially under Haar-random projective measurements with respect to the number of qudits. These results provide theoretical support for the reliable use of PEPS and PEPO in practical quantum information processing.

Mixtures, Markov bridges and the matrix product ansatz

Authors: Davide Gabrielli, Federica Iacovissi

arXiv ID: 2509.16455 | Date: 2025-09-19

Abstract: We give a probabilistic characterization of the set of measures that can be represented by the matrix product ansatz. By suitably enlarging the state space, we show that a probability measure can be described in terms of non negative matrices by the {\it Matrix Product Ansatz}, if and only if it can be written as a mixture of inhomogeneous product measures where the mixing law is a Markov bridge. We give a constructive procedure to identify such probabilistic features. We illustrate the result by examples and show that existing probabilistic representations of the invariant measures of non equilibrium interacting particle systems can be obtained from the matrix product ansatz by this general procedure.

Locally Purified Maximally Mixed States At Scale: Entanglement Pruning and Symmetries

Authors: Amit Jamadagni, Eugene Dumitrescu

arXiv ID: 2509.16439 | Date: 2025-09-19

Abstract: Locally Purified Density Operators (LPDOs) are state-of-the-art tensor network ansatze candidates that efficiently represent mixed quantum states at scale. However, given their non-uniqueness, their representational complexity is generally sub-optimal in practical computations. In this work we perform a comprehensive numerical and analytical analysis and resolve this issue in the experimentally relevant limit where noise depolarizes the density operator into a maximally mixed state. To resolve the sub-optimality issue, we analyze two numerical tools, one analytic method, and detail the relations between them. The numerical tools used are fidelity-preserving truncations and isometric gauge transformations leveraging Riemannian optimizations over entropic objective functions. In addition, by invoking the injectivity and symmetry constraints of the maximally mixed LPDO, we also present analytical closed-form expressions for the disentangler and discuss their relation to numerical optimizers. Our work shows how, by minimizing the resources required to represent key states of practical interest in experiment, the efficiency of tensor network algorithms can be substantially increased. This paves the path for uncovering tensor network's fundamental scalability limits and latent potential in representing the wide locus of mixed quantum states that are accessible on near-term quantum devices.

Entanglement Asymmetry for Higher and Noninvertible Symmetries

Authors: Francesco Benini, Pasquale Calabrese, Michele Fossati, Amartya Harsh Singh, Marco Venuti

arXiv ID: 2509.16311 | Date: 2025-09-19

Abstract: Entanglement asymmetry is an observable in quantum systems, constructed using quantum-information methods, suited to detecting symmetry breaking in states -- possibly out of equilibrium -- relative to a subsystem. In this paper we define the asymmetry for generalized finite symmetries, including higher-form and noninvertible ones. To this end, we introduce a "symmetrizer" of (reduced) density matrices with respect to the CC^*-algebra of symmetry operators acting on the subsystem Hilbert space. We study in detail applications to (1+1)-dimensional theories: First, we analyze spontaneous symmetry breaking of noninvertible symmetries, confirming that distinct vacua can exhibit different physical properties. Second, we compute the asymmetry of certain excited states in conformal field theories (including the Ising CFT), when the subsystem is either the full circle or an interval therein. The relevant symmetry algebras to consider are the fusion, tube, and strip algebras. Finally, we comment on the case that the symmetry algebra is a (weak) Hopf algebra.

Exploring confinement transitions in Z2\mathbb{Z}_2 lattice gauge theories with dipolar atoms beyond one dimension

Authors: Matjaž Kebrič, Lin Su, Alexander Douglas, Michal Szurek, Ognjen Marković, Ulrich Schollwöck, Annabelle Bohrdt, Markus Greiner, Fabian Grusdt

arXiv ID: 2509.16200 | Date: 2025-09-19

Abstract: Confinement of particles into bound states is a phenomenon spanning from high-energy to condensed matter physics, which can be studied in the framework of lattice gauge theories (LGTs). Achieving a comprehensive understanding of confinement continues to pose a major challenge, in particular at finite matter density and in the presence of strong quantum fluctuations. State-of-the-art quantum simulators constitute a promising platform to address this problem. Here we study confinement in coupled chains of Z2\mathbb{Z}_2 LGTs coupled to matter fields, that can be mapped to a mixed-dimensional (mixD) XXZ model. We perform large-scale numerical matrix-product state calculations to obtain the phase diagram of this model, in which we uncover striped phases formed by the Z2\mathbb{Z}_2 charges that can be melted at finite temperature or by increasing the tunneling rate. To explore this setting experimentally, we use our quantum simulator constituted by erbium atoms with dipolar interactions in a quantum gas microscope, and observe the predicted melting of a stripe phase by increasing the particle tunneling rate. Our explorative experimental studies of thermal deconfinement of Z2\mathbb{Z}_2 charges motivate our further theoretical study of the mixD Z2\mathbb{Z}_2 LGT, in which we predict a confined meson gas at finite temperature and low magnetization where thermal fluctuations destroy stripes but enable spontaneous commensurate spin order. Overall, we demonstrate that our platform can be used to study confinement in Z2\mathbb{Z}_2 LGTs coupled to matter fields, including long-range interactions and beyond one dimension, paving the way for future research of confinement in the quantum many-body regime.

Incorporating Coulomb interactions with fixed charges in Moment Tensor Potentials and Equivariant Tensor Network Potentials

Authors: Dmitry Korogod, Olga Chalykh, Max Hodapp, Nikita Rybin, Ivan S. Novikov, Alexander V. Shapeev

arXiv ID: 2509.15907 | Date: 2025-09-19

Abstract: In this work, we incorporate long-range electrostatic interactions in the form of the Coulomb model with fixed charges into the functional form of short-range machine-learning interatomic potentials (MLIPs), particularly in the Moment Tensor Potential and Equivariant Tensor Network potential. We show that explicit incorporation of the Coulomb interactions with fixed charges leads to a significant reduction of energy fitting errors, namely, more than four times, of short-range MLIPs trained on organic dimers of charged molecules. Furthermore, with our long-range models we demonstrate a significant improvement in the prediction of the binding curves of the organic dimers of charged molecules. Finally, we show that the results calculated with MLIPs are in good correspondence with those obtained with density functional theory for organic dimers of charged molecules.

Dispersion Relations in Two- and Three-Dimensional Quantum Systems

Authors: Valeriia Bilokon, Elvira Bilokon, Illya Lukin, Andrii Sotnikov, Denys Bondar

arXiv ID: 2509.15483 | Date: 2025-09-18

Abstract: Extracting momentum-resolved excitation spectra in strongly correlated quantum systems remains a major challenge, especially beyond one spatial dimension. We present an efficient tensor-network approach to compute dispersion relations via imaginary-time evolution within the infinite projected entangled-pair states (iPEPS) framework. Benchmarking on the transverse-field Ising model, the method successfully captures dispersion relations in both paramagnetic and ferromagnetic phases for two- and three-dimensional lattices, achieving strong agreement with series expansion methods, where these are applicable. Crucially, this work presents the first demonstration of dispersion relation calculations for three-dimensional quantum lattice models - a long-standing computational challenge that opens entirely new research frontiers. The method demonstrates remarkable efficiency, requiring only modest computational resources while maintaining high accuracy across wide parameter ranges. Its broad applicability makes it a powerful tool for quantum simulation, photonic material design, and quantum information platforms requiring precise momentum-resolved spectra.

Living on the edge: a non-perturbative resolution to the negativity of bulk entropies

Authors: Stefano Antonini, Luca V. Iliesiu, Pratik Rath, Patrick Tran

arXiv ID: 2509.15295 | Date: 2025-09-18

Abstract: Lin, Maldacena, Rozenberg, and Shan (LMRS) presented a new information paradox in black hole physics by noticing that the entanglement and Rényi entropies in a two-sided black hole can become negative when the geometry contains a very large number of matter excitations behind the black hole horizon. While originally this puzzle was presented in the context of BPS two-sided black holes in two-dimensional supergravity, the negativity in fact persists for more general two-sided black holes in the presence of a large number of matter excitations. Since the entanglement and Rényi entropies in ordinary quantum systems cannot be negative, resolving this puzzle is a necessary step towards understanding the quantum mechanical description of black holes. In this paper, we explain how to address the entanglement negativity puzzle, both in the original setting discussed by LMRS and in more general non-supersymmetric settings, by summing over all non-perturbative contributions to the gravitational path integral. We then interpret this result from the point of view of a dual matrix integral, which we use to extend our analysis beyond the regime of validity of the genus re-summation performed in the gravitational path integral. In this regime, positivity is rescued by new saddles of the matrix integral, a one-eigenvalue instanton and a two-eigenvalue instanton. Finally, we formulate a similar puzzle and its resolution using random tensor network techniques.

Competing and Intertwined Orders in Boson-Doped Mott Antiferromagnets

Authors: Xin Lu, Jia-Xin Zhang, Lukas Homeier, Hong-Chen Jiang, Shou-Shu Gong, D. N. Sheng, Zheng-Yu Weng

arXiv ID: 2509.15215 | Date: 2025-09-18

Abstract: Inspired by the recent experimental advances in cold atom quantum simulators, we explore the experimentally implemented bosonic tt-tt'-JJ model on the square lattice using large-scale density matrix renormalization group simulations. By tuning the doping level δδ and hopping ratio t/tt'/t, we uncover six distinct quantum phases, several of which go far beyond the conventional paradigm of phase-coherent superfluidity (SF) expected for bosonic systems. In particular, in the presence of antiferromagnetic (AFM) order, doped holes are tightly bound into pairs, giving rise to a pair density wave (PDW) phase at low doping and small t/t|t'/t|, which is suppressed on the t<0t'<0 side, resulting in a disordered PDW state that lacks coherence of either individual bosons or pairs. Upon further doping, bosons can regain phase coherence and form a SF* state, characterized by condensation at emergent incommensurate momenta concurrent with an incommensurate magnetic order. On the t>0t'>0 side, the sign-induced kinetic frustration inherently disfavors local AFM correlations, leading to a phase separation in which doped holes cluster into ferromagnetic (FM) domains spatially separated by undoped AFM regions. Upon further doping, this inhomogeneous state evolves into a uniform SF + xyxy-FM phase. Finally, we propose a concrete experimental scheme to realize both signs of t/tt'/t in Rydberg tweezer arrays, with an explicit mapping between model parameters and experimentally accessible regimes. Our results reveal competing and intertwined orders in doped antiferromagnets, which are relevant to central issues in high-TcT_c superconductivity, reflecting the frustrated interplay between doped holes and spin background.

A causality-based divide-and-conquer algorithm for nonequilibrium Green's function calculations with quantics tensor trains

Authors: Ken Inayoshi, Maksymilian Środa, Anna Kauch, Philipp Werner, Hiroshi Shinaoka

arXiv ID: 2509.15028 | Date: 2025-09-18

Abstract: We propose a causality-based divide-and-conquer algorithm for nonequilibrium Green's function calculations with quantics tensor trains. This algorithm enables stable and efficient extensions of the simulated time domain by exploiting the causality of Green's functions. We apply this approach within the framework of nonequilibrium dynamical mean-field theory to the simulation of quench dynamics in symmetry-broken phases, where long-time simulations are often required to capture slow relaxation dynamics. We demonstrate that our algorithm allows to extend the simulated time domain without a significant increase in the cost of storing the Green's function.

Scaling Hybrid Quantum-HPC Applications with the Quantum Framework

Authors: Srikar Chundury, Amir Shehata, Seongmin Kim, Muralikrishnan Gopalakrishnan Meena, Chao Lu, Kalyana Gottiparthi, Eduardo Antonio Coello Perez, Frank Mueller, In-Saeng Suh

arXiv ID: 2509.14470 | Date: 2025-09-17

Abstract: Hybrid quantum-high performance computing (Q-HPC) workflows are emerging as a key strategy for running quantum applications at scale in current noisy intermediate-scale quantum (NISQ) devices. These workflows must operate seamlessly across diverse simulators and hardware backends since no single simulator offers the best performance for every circuit type. Simulation efficiency depends strongly on circuit structure, entanglement, and depth, making a flexible and backend-agnostic execution model essential for fair benchmarking, informed platform selection, and ultimately the identification of quantum advantage opportunities. In this work, we extend the Quantum Framework (QFw), a modular and HPC-aware orchestration layer, to integrate multiple local backends (Qiskit Aer, NWQ-Sim, QTensor, and TN-QVM) and a cloud-based quantum backend (IonQ) under a unified interface. Using this integration, we execute a number of non-variational as well as variational workloads. The results highlight workload-specific backend advantages: while Qiskit Aer's matrix product state excels for large Ising models, NWQ-Sim not only leads on large-scale entanglement and Hamiltonian but also shows the benefits of concurrent subproblem execution in a distributed manner for optimization problems. These findings demonstrate that simulator-agnostic, HPC-aware orchestration is a practical path toward scalable, reproducible, and portable Q-HPC ecosystems, thereby accelerating progress toward demonstrating quantum advantage.

Antiferromagnetic resonance and two-magnon absorption in an XXZ-chain antiferromagnet Cs2CoCl4

Authors: T. A. Soldatov, A. I. Smirnov

arXiv ID: 2509.13953 | Date: 2025-09-17

Abstract: Magnetic excitations of the exchange-dipole quasi 1D XXZ antiferromagnet are studied in the ordered phase. We observe a transformation of the electron spin resonance (ESR) spectrum when crossing the Néel temperature near 0.2 K. The single-mode ESR of a correlated XXZ chain transforms in the multi-mode spectrum in the ordered phase. The multi-mode spectrum consists mainly of the intensive mode of a single correlated chain, which is surrounded and/or indented by numerous weak satellites. The number of securely fixed modes is eight at magnetic field parallel b-axis and twelve at magnetic field parallel a-axis. Besides of the multi-mode resonance observed at the transverse polarization of the microwave and static magnetic fields, we reveal a wide band of absorption by (k,-k)- pairs of quasiparticles at the longitudinal polarization. This kind of absorption of microwaves occurs both in the ordered and specific spin-liquid phases, revealing the presence of quasiparticles in the specific spin-liquid phase.

Closely competing valence bond crystal orders in the ground state of the spin-12\frac{1}{2} antiferromagnetic Heisenberg model on the pyrochlore lattice: a large scale unrestricted variational study

Authors: Rong Cheng, Tao Li

arXiv ID: 2509.13746 | Date: 2025-09-17

Abstract: The spin-12\frac{1}{2} antiferromagnetic Heisenberg model on the pyrochlore lattice(PAFH) is arguably the most well known strongly frustrated quantum magnet in three spatial dimension. However, due to the rapid scaling of Hilbert space with the linear size of such a three dimensional system, the nature of its ground state in the thermodynamic limit remains elusive after about 30 years' intense debate. Here we apply a recently developed powerful algorithm to perform large scale unrestricted variational optimization of the ground state of the spin-12\frac{1}{2} PAFH from the resonating valence bond(RVB) theory perspective. We find a highly competitive candidate ground state of the system. This novel state features a maximally resonating valence bond crystal(VBC) pattern with 2a1×2a2×2a32\vec{a}_{1}\times2\vec{a}_{2}\times2\vec{a}_{3} periodicity. There are at least four levels of hierarchical structure in such a VBC state, with the first and the second level of hierarchy related to the breaking of the inversion and the translational symmetry. Intriguingly, we find that within the RVB framework such a maximally resonating VBC state is almost degenerate with a recently proposed VBC state that is obtained from dressing hard hexagon covering of the pyrochlore lattice, although they have very different structures. We also find that further symmetry breaking will occur in the dressed hard hexagon VBC state under unrestricted optimization, which results in strong disparity in S^u2\langle \hat{\mathbf{S}}^{2}_{u} \rangle for up and down tetrahedrons as we observe in the maximally resonating VBC state. We show that the maximally resonating VBC state found here will be favored by a tiny next-neighboring exchange coupling over the dressed hard hexagon covering VBC state.

Evaluating the Limits of QAOA Parameter Transfer at High-Rounds on Sparse Ising Models With Geometrically Local Cubic Terms

Authors: Elijah Pelofske, Marek Rams, Andreas Bärtschi, Piotr Czarnik, Paolo Braccia, Lukasz Cincio, Stephan Eidenbenz

arXiv ID: 2509.13528 | Date: 2025-09-16

Abstract: The emergent practical applicability of the Quantum Approximate Optimization Algorithm (QAOA) for approximate combinatorial optimization is a subject of considerable interest. One of the primary limitations of QAOA is the task of finding a set of good parameters. Parameter transfer is a phenomenon where QAOA angles trained on problem instances that are self-similar tend to perform well for other problem instances from that similar class. This suggests a potentially highly efficient and scalable non-variational learning method for QAOA angle finding. We systematically study QAOA parameter transferability from small problems (16, 27 qubits) onto large problem instances (up to 156 qubits) for heavy-hex graph Ising models with geometrically local higher order terms using the Julia based QAOA simulation tool JuliQAOA to perform classical angle finding for up to 49 QAOA layers. Parameter transfer of the fixed angles is validated using a combination of full statevector, Projected Entangled Pair States, Matrix Product State, and LOWESA numerical simulations. We find that the QAOA parameter transfer from single instances applied to unseen problem instances does not in general provide monotonically improving performance as a function of p - there are many cases where the performance temporarily decreases as a function of p - but despite this the transferred angles have a general trend of improved expectation value as the QAOA depth increases, in many cases converging close to the true ground-state energy of the 100+ qubit instances. We also sample the hardware-compatible Ising models using the ensemble of fixed QAOA angles on several superconducting qubit IBM Quantum processors with 127, 133, and 156 qubits. We find continuous solution quality improvement of the hardware-compatible QAOA circuits run on the IBM NISQ processors up to p=5 on ibm_fez, p=9 on ibm_torino, and p=10 on ibm_pittsburgh.

Bilayer graphene quantum dots as a quantum simulator of Haldane topological quantum matter

Authors: Daniel Miravet, Hassan Allami, Marek Korkusinski, Pawel Hawrylak

arXiv ID: 2509.13495 | Date: 2025-09-16

Abstract: We demonstrate here that a chain of Bilayer Graphene Quantum Dots (BLGQD) can realize topological quantum matter by effectively simulating a spin-1 chain that hosts the Haldane phase within a specific range of parameters. We describe a chain of BLGQD with two electrons each using an atomistic tight-binding model combined with the exact diagonalization technique to solve the interacting few-electron problem. Coulomb interactions and valley mixing effects are treated within the same microscopic framework, allowing us to systematically investigate spin and valley polarization transitions as functions of interaction strength and external tuning parameters. We calculate the low energy states for single and double QDs as a function of the number of electrons, identifying regimes of highly correlated multi-electron states. We confirm the presence of a spin-one ground state for two electrons. Then, we explore two coupled QDs with 4 electrons and extend the analysis to QD arrays. Using a mapping of the BLGQD chain to an effective bilinear-biquadratic (BLBQ) spin model, we demonstrate that BLGQD arrays can work as a quantum simulator for one-dimensional spin chains with emergent many-body topological phases.

A Tensor Train-Based Isogeometric Solver for Large-Scale 3D Poisson Problems on Complex Geometries

Authors: Quoc Thai Tran, Duc P. Truong, Kim Ø. Rasmussen, Boian Alexandrov

arXiv ID: 2509.13224 | Date: 2025-09-16

Abstract: We introduce a three-dimensional (3D) fully tensor train (TT)-assembled isogeometric analysis (IGA) framework, TT-IGA, for solving partial differential equations (PDEs) on complex geometries. Our method reformulates IGA discrete operators into TT format, enabling efficient compression and computation while retaining geometric flexibility and accuracy. Unlike previous low-rank approaches that typically rely on structured domains, our framework accommodates general 3D geometries through low-rank TT representations of both the geometry mapping and the PDE discretization. We demonstrate the effectiveness of the proposed TT-IGA framework on the 3D Poisson equation, achieving substantial reductions in memory usage and computational cost without compromising solution quality.

From higher-order moments to time correlation functions in strongly correlated systems: A DMRG-based memory kernel coupling theory

Authors: Yunhao Liu, Wenjie Dou

arXiv ID: 2509.13140 | Date: 2025-09-16

Abstract: We introduce a hybrid approach for computing dynamical observables in strongly correlated systems using higher-order moments. This method integrates memory kernel coupling theory (MKCT) with the density matrix renormalization group (DMRG), extending our recent work on MKCT to strongly correlated systems. The method establishes that correlation functions can be derived from the moments. Within our framework, operators and wavefunctions are represented as matrix product operators (MPOs) and matrix product states (MPSs), respectively. Crucially, the repeated application of the Liouville operator is achieved through an iterative procedure analogous to the DMRG algorithm itself. We demonstrate the effectiveness and efficiency of MKCT-DMRG by computing the spectral function of the Hubbard model. Furthermore, we successfully apply the method to compute the electronic friction in the Hubbard-Holstein model. In all cases, the results show excellent agreement with time-dependent DMRG (TD-DMRG) benchmarks. The advantage of MKCT-DMRG over TD-DMRG is the computational efficiency, which avoids expensive real-time propagation in TD-DMRG. These findings establish MKCT-DMRG as a promising and accurate framework for simulating challenging dynamical properties in strongly correlated quantum systems.

Tensor Train Completion from Fiberwise Observations Along a Single Mode

Authors: Shakir Showkat Sofi, Lieven De Lathauwer

arXiv ID: 2509.18149 | Date: 2025-09-16

Abstract: Tensor completion is an extension of matrix completion aimed at recovering a multiway data tensor by leveraging a given subset of its entries (observations) and the pattern of observation. The low-rank assumption is key in establishing a relationship between the observed and unobserved entries of the tensor. The low-rank tensor completion problem is typically solved using numerical optimization techniques, where the rank information is used either implicitly (in the rank minimization approach) or explicitly (in the error minimization approach). Current theories concerning these techniques often study probabilistic recovery guarantees under conditions such as random uniform observations and incoherence requirements. However, if an observation pattern exhibits some low-rank structure that can be exploited, more efficient algorithms with deterministic recovery guarantees can be designed by leveraging this structure. This work shows how to use only standard linear algebra operations to compute the tensor train decomposition of a specific type of ``fiber-wise" observed tensor, where some of the fibers of a tensor (along a single specific mode) are either fully observed or entirely missing, unlike the usual entry-wise observations. From an application viewpoint, this setting is relevant when it is easier to sample or collect a multiway data tensor along a specific mode (e.g., temporal). The proposed completion method is fast and is guaranteed to work under reasonable deterministic conditions on the observation pattern. Through numerical experiments, we showcase interesting applications and use cases that illustrate the effectiveness of the proposed approach.

RandomMeas.jl: A Julia Package for Randomized Measurements in Quantum Devices

Authors: Andreas Elben, Benoît Vermersch

arXiv ID: 2509.12749 | Date: 2025-09-16

Abstract: We introduce RandomMeas.jl, a modular and high-performance open-source software package written in Julia for implementing and analyzing randomized measurement protocols in quantum computing. Randomized measurements provide a powerful framework for extracting properties of quantum states and processes such as expectation values, entanglement, and fidelities using simple experimental procedures combined with classical post-processing, most prominently via the classical shadow formalism. RandomMeas.jl covers the full randomized measurement workflow, from the generation of measurement settings for use on a quantum computer, the optional classical simulation of randomized measurements with tensor networks, to a suite of estimators for physical properties based on classical shadows. The package includes advanced features such as robust and shallow shadow techniques, batch estimators, and built-in statistical uncertainty estimation. Its unified, composable design enables the scalable application and further development of randomized measurements protocols across theoretical and experimental contexts.

Integrated Software/Hardware Execution Models for High-Accuracy Methods in Chemistry

Authors: Nicholas Bauman, Ajay Panyala, Libor Veis, Jiri Brabec, Paul Rigor, Randy Meyer, Skyler Windh, Craig Warner, Tony Brewer, Karol Kowalski

arXiv ID: 2510.01205 | Date: 2025-09-15

Abstract: The effective deployment and application of advanced methodologies for quantum chemistry is inherently linked to the optimal usage of emerging and highly diversified computational resources. This paper examines the synergistic utilization of Micron memory technologies and Azure Quantum Element cloud computing in Density Matrix Renormalization Group (DMRG) simulations leveraging coupled-cluster (CC) downfolded/effective Hamiltonians based on the double unitary coupled cluster (DUCC) Ansatz. We analyze the performance of the DMRG-DUCC workflow, emphasizing the proper choice of hardware that reflects the numerical overheads associated with specific components of the workflow. We report a hybrid approach that takes advantage of Micron CXL hardware for the memory capacity intensive CC downfolding phase while employing AQE cloud computing for the less resource-intensive DMRG simulations. Furthermore, we analyze the performance of the scalable ExaChem suite of electronic simulations conducted on Micron prototype systems.

Topological Phase Diagram of Generalized SSH Models with Interactions

Authors: Yuxiao Hang, Stephan Haas

arXiv ID: 2509.12373 | Date: 2025-09-15

Abstract: We investigate interacting Su-Schrieffer-Heeger (SSH) chains with two- and three-site unit cells using density matrix renormalization group (DMRG) simulations. By selecting appropriate filling fractions and sweeping across interaction strength \( J_z \) and dimerization \( δ\), we map out their phase diagrams and identify transition lines via entanglement entropy and magnetization measurements. In the two-site model, we observe the emergence of an interaction-induced antiferromagnetic intermediate phase between the topologically trivial and non-trivial regimes, as well as a critical region at negative \( J_z \) with suppressed magnetization and finite-size scaling of entanglement entropy. In contrast, the three-site model lacks an intermediate phase and exhibits asymmetric edge localization and antiferromagnetic ordering in both positive and negative \( J_z \) regimes. We further examine the response of edge states to Ising perturbations. In the two-site model, zero-energy edge modes are topologically protected and remain robust up to a finite interaction strength. However, in the three-site model, where the edge states reside at finite energy, this protection breaks down. Despite this, the edge-localized nature of these states survives in the form of polarized modes whose spatial profiles reflect the non-interacting limit.

A graphical diagnostic of topological order using ZX calculus

Authors: Sergi Mas-Mendoza, Richard D. P. East, Michele Filippone, Adolfo G. Grushin

arXiv ID: 2509.12355 | Date: 2025-09-15

Abstract: Establishing a universal diagnostic of topological order remains an open theoretical challenge. In particular, diagnosing long-range entanglement through the entropic area law suffers from spurious contributions, failing to unambiguously identify topological order. Here we devise a protocol based on the ZX calculus, a graphical tensor network, to determine the topological order of a state circumventing entropy calculations. The protocol takes as input real-space bipartitions of a state and returns a ZX contour diagram, DA\mathcal{D}_{\partial A}, displaying long-range graph connectivity only for long-range entangled states. We validate the protocol by showing that the contour diagrams of the toric and color codes are equivalent except for the number of non-local nodes, which differentiates their topological order. The number of these nodes is robust to the choice of the boundary and ground-state superposition, and they are absent for trivial states, even those with spurious entropy contributions. Our results single out ZX calculus as a tool to detect topological long-range entanglement by leveraging the advantages of diagrammatic reasoning against entropic diagnostics.

Higher-Form Anomalies on Lattices

Authors: Yitao Feng, Ryohei Kobayashi, Yu-An Chen, Shinsei Ryu

arXiv ID: 2509.12304 | Date: 2025-09-15

Abstract: Higher-form symmetry in a tensor product Hilbert space is always emergent: the symmetry generators become genuinely topological only when the Gauss law is energetically enforced at low energies. In this paper, we present a general method for defining the 't Hooft anomaly of higher-form symmetries in lattice models built on a tensor product Hilbert space. In (2+1)D, for given Gauss law operators realized by finite-depth circuits that generate a finite 1-form GG symmetry, we construct an index representing a cohomology class in H4(B2G,U(1))H^4(B^2G, U(1)), which characterizes the corresponding 't Hooft anomaly. This construction generalizes the Else-Nayak characterization of 0-form symmetry anomalies. More broadly, under the assumption of a specified formulation of the pp-form GG symmetry action and Hilbert space structure in arbitrary dd spatial dimensions, we show how to characterize the 't Hooft anomaly of the symmetry action by an index valued in Hd+2(Bp+1G,U(1))H^{d+2}(B^{p+1}G, U(1)).

From hidden order to skyrmions: Quantum Hall states in an extended Hofstadter-Fermi-Hubbard model

Authors: Fabian J. Pauw, Ulrich Schollwöck, Nathan Goldman, Sebastian Paeckel, Felix A. Palm

arXiv ID: 2509.12184 | Date: 2025-09-15

Abstract: The interplay between topology and strong interactions gives rise to a variety of exotic quantum phases, including fractional quantum Hall (FQH) states and their lattice analogs - fractional Chern insulators (FCIs). Such topologically ordered states host fractionalized excitations and, for spinful systems, are often accompanied by ferromagnetism and skyrmions. Here, we study a Hofstadter-Hubbard model of spinful fermions on a square lattice, extended by nearest-neighbor interactions. Using large-scale density matrix renormalization group (DMRG) simulations, we demonstrate the emergence of a spin-polarized 13\frac{1}{3}-Laughlin-like FCI phase, characterized by a quantized many-body Chern number, a finite charge gap, and hidden off-diagonal long-range order. We further investigate the quantum Hall ferromagnet at ν=1ν=1 and its skyrmionic excitations upon doping. In particular, we find that nearest-neighbor repulsion is sufficient to stabilize both particle- and hole-skyrmions in the ground state around ν=1ν=1, whereas we do not find such textures around ν=13ν=\frac{1}{3}. The diagnostic toolbox presented in this work, based on local densities, correlation functions, and spin-resolved observables, is directly applicable in quantum gas microscopy experiments. Our results open new pathways for experimental exploration of FCIs with spin textures in both ultracold atom and electronic systems.

Spectral Small-Incremental-Entangling: Breaking Quasi-Polynomial Complexity Barriers in Long-Range Interacting Systems

Authors: Donghoon Kim, Yusuke Kimura, Hugo Mackay, Yosuke Mitsuhashi, Hideaki Nishikawa, Carla Rubiliani, Cheng Shang, Ayumi Ukai, Tomotaka Kuwahara

arXiv ID: 2509.12014 | Date: 2025-09-15

Abstract: How the detailed structure of quantum complexity emerges from quantum dynamics remains a fundamental challenge highlighted by advances in quantum simulators and information processing. The celebrated Small-Incremental-Entangling (SIE) theorem provides a universal constraint on the rate of entanglement generation, yet it leaves open the problem of fully characterizing fine entanglement structures. Here we introduce the concept of Spectral-Entangling strength, which captures the structural entangling power of an operator, and establish a spectral SIE theorem: a universal speed limit for R'enyi entanglement growth at α1/2α\ge 1/2, revealing a robust 1/s21/s^2 decay threshold in the entanglement spectrum. Remarkably, our bound at α=1/2α=1/2 is both qualitatively and quantitatively optimal, defining the universal threshold beyond which entanglement growth becomes unbounded. This exposes the detailed structure of Schmidt coefficients and enables rigorous truncation-based error control, linking entanglement structure to computational complexity. Building on this, we derive a generalized entanglement area law under an adiabatic-path condition, extending a central principle of quantum many-body physics to general interactions. As a concrete application, we show that one-dimensional long-range interacting systems admit polynomial bond-dimension approximations for ground, time-evolved, and thermal states, thereby closing the long-standing quasi-polynomial gap and demonstrating that such systems can be simulated efficiently with tensor-network methods. By explicitly controlling R'enyi entanglement, we obtain a rigorous, a priori error guarantee for the time-dependent density-matrix renormalization-group algorithm. Overall, our results extend the SIE theorem to the spectral domain and establish a unified framework that unveils the detailed and universal structure underlying quantum complexity.

Characterizing Scaling Trends of Post-Compilation Circuit Resources for NISQ-era QML Models

Authors: Rupayan Bhattacharjee, Pau Escofet, Santiago Rodrigo, Sergi Abadal, Carmen G. Almudever, Eduard Alarcón

arXiv ID: 2509.11980 | Date: 2025-09-15

Abstract: This work investigates the scaling characteristics of post-compilation circuit resources for Quantum Machine Learning (QML) models on connectivity-constrained NISQ processors. We analyze Quantum Kernel Methods and Quantum Neural Networks across processor topologies (linear, ring, grid, star), focusing on SWAP overhead, circuit depth, and two-qubit gate count. Our findings reveal that entangling strategy significantly impacts resource scaling, with circular and shifted circular alternating strategies showing steepest scaling. Ring topology demonstrates slowest resource scaling for most QML models, while Tree Tensor Networks lose their logarithmic depth advantage after compilation. Through fidelity analysis under realistic noise models, we establish quantitative relationships between hardware improvements and maximum reliable qubit counts, providing crucial insights for hardware-aware QML model design across the full-stack architecture.

An Inexact Tensor-Train Primal-Dual Interior-Point Method for Semidefinite Programs

Authors: Frederik Kelbel, Sergey Dolgov, Dante Kalise, Alessandra Russo

arXiv ID: 2509.11890 | Date: 2025-09-15

Abstract: In this work, we introduce an interior-point method that employs tensor decompositions to efficiently represent and manipulate the variables and constraints of semidefinite programs, targeting problems where the solutions may not be low-rank but admit low-tensor-train rank approximations. Our method maintains approximate superlinear convergence despite inexact computations in the tensor format and leverages a primal-dual infeasible interior-point framework. In experiments on Maximum Cut, Maximum Stable Set, and Correlation Clustering, the tensor-train interior point method handles problems up to size 2122^{12} with duality gaps around 10610^{-6} in approximately 1.5~h and using less than 2~GB of memory, outperforming state-of-the-art solvers on larger instances. Moreover, numerical evidence indicates that tensor-train ranks of the iterates remain moderate along the interior-point trajectory, explaining the scalability of the approach. Tensor-train interior point methods offer a promising avenue for problems that lack traditional sparsity or low-rank structure, exploiting tensor-train structures instead.

Optimizing Quantum Photonic Integrated Circuits using Differentiable Tensor Networks

Authors: Mathias Van Regemortel, Thomas Van Vaerenbergh

arXiv ID: 2509.11861 | Date: 2025-09-15

Abstract: Recent reports of large photonic nonlinearities in integrated photonic devices, using the strong excitonic light-matter coupling in semiconductors, necessitate a tailored design framework for quantum processing in the limit of low photon occupation. We present a gradient-based optimization method for quantum photonic integrated circuits, which are composed of nonlinear unitary coupling gates and stochastic, nonunitary components for sampling the photonic losses. As core of our method, differentiable tensor-networks are leveraged, which are accurate in the regime of low photonic occupation and modest intermode entanglement. After characterizing the circuit gate architecture with field simulations of GaAs-based samples, we demonstrate the applicability of our method by optimizing quantum photonic circuits for two key use cases: integrated designs for quantum optical state preparation and tailored optimal readout for quantum phase sensing.

Generalization of the Affleck-Kennedy-Lieb-Tasaki Model for Quantum Ferromagnetism

Authors: Isao Maruyama, Shin Miyahara

arXiv ID: 2509.11537 | Date: 2025-09-15

Abstract: We generalize the Affleck-Kennedy-Lieb-Tasaki model to a spin-\(S\) ferromagnetic model with exactly-written ground states, known as the partially-magnetized valence bond solid (VBS) states with magnetization m=(S1)/Sm=(S-1)/S. We find that the VBS state and an antiferromagnetic ground state with magnetization m=0m=0 are degenerate for S=3/2S=3/2 and S=2S=2 by using the Lanczos method and the density matrix renormalization group method (DMRG). However, increasing SS, the magnetization of the ground states is uniquely determined as the fraction m=(S1)/Sm=(S-1)/S. This is not just a ferromagnet, but a quantum ferromagnet due to quantum entanglement inherent in VBS states. In the low-energy excitation spectrum, we find the coexistence of the Haldane gap and Goldstone-like ferromagnetic magnon excitation. This ``magnetic chimera'' clearly appears under a finite magnetic field. Finally, we discuss an application to the measurement-based quantum computation and an extension of the Haldane's conjecture.

Vanishing Signatures, Orbit Closure, and the Converse of the Holant Theorem

Authors: Jin-Yi Cai, Ben Young

arXiv ID: 2509.10991 | Date: 2025-09-13

Abstract: Valiant's Holant theorem is a powerful tool for algorithms and reductions for counting problems. It states that if two sets F\mathcal{F} and G\mathcal{G} of tensors (a.k.a. constraint functions or signatures) are related by a \emph{holographic transformation}, then F\mathcal{F} and G\mathcal{G} are \emph{Holant-indistinguishable}, i.e., every tensor network using tensors from F\mathcal{F}, resp. from G\mathcal{G}, contracts to the same value. Xia (ICALP 2010) conjectured the converse of the Holant theorem, but a counterexample was found based on \emph{vanishing} signatures, those which are Holant-indistinguishable from 0. We prove two near-converses of the Holant theorem using techniques from invariant theory. (I) Holant-indistinguishable F\mathcal{F} and G\mathcal{G} always admit two sequences of holographic transformations mapping them arbitrarily close to each other, i.e., their GLq\text{GL}_q-orbit closures intersect. (II) We show that vanishing signatures are the only true obstacle to a converse of the Holant theorem. As corollaries of the two theorems we obtain the first characterization of homomorphism-indistinguishability over graphs of bounded degree, a long standing open problem, and show that two graphs with invertible adjacency matrices are isomorphic if and only if they are homomorphism-indistinguishable over graphs with maximum degree at most three. We also show that Holant-indistinguishability is complete for a complexity class \textbf{TOCI} introduced by Lysikov and Walter, and hence hard for graph isomorphism.

Onset of Bjorken Flow in Quantum Evolution of the Massive Schwinger Model

Authors: Haiyang Shao, Shile Chen, Shuzhe Shi

arXiv ID: 2509.10855 | Date: 2025-09-13

Abstract: The onset of hydrodynamics in the hot medium created in relativistic heavy-ion collisions is a crucial theoretical question. A first-principle simulation requires a real-time, non-perturbative calculation of the quantum system. In this Letter, we perform such simulations using the tensor network method, which enables large-scale quantum many-body simulations by retaining only the most essential quantum states for collective behaviors. We focus on the massive Schwinger model, a low-dimensional analog of quantum chromodynamics (QCD), as they share important properties such as confinement and chiral symmetry breaking. Starting from an initial state that puts a localized excitation atop the vacuum and mimics the energy deposition from colliding nuclei, we observe hydrodynamic behavior consistent with Bjorken flow in all relevant degrees of freedom: energy density, fluid velocity, and bulk pressure. The time scale for hydrodynamic onset aligns with the thermalization time of the quantum distribution function.

Collective motion in the massive Schwinger model via Tensor Network

Authors: Haiyang Shao, Shile Chen, Shuzhe Shi

arXiv ID: 2509.10835 | Date: 2025-09-13

Abstract: We simulate the real-time dynamics of a massive Schwinger model using the Time-Evolving Block Decimation tensor network algorithm. Starting from a non-equilibrium initial state with localized energy excitation on top of vacuum, we track the subsequent evolution to investigate two distinct physical phenomena. First, by analyzing the system's energy-momentum tensor, we show that this system exhibits hydrodynamic behavior analogous to Bjorken flow at large coupling-to-mass ratio, a signature that diminishes as the coupling weakens, or mass increases. Second, by examining the evolution of the electric field and charge density, we observe the signal of spontaneous parity symmetry breaking phase transition in a dynamical system. The parity-restored regime is marked by ''string breaking'' and efficient charge screening, while the parity-broken regime displays stable propagation of nearly free charges and persistent electric fields connecting them.

Higher tensor categories and their extensions: notes from the Scottish Talbot On Algebra and Topology

Authors: Diogo Andrade, Julia Bierent, Jennifer Brown, Tudor Caba, Matthew Cellot, Jonathan Davies, Adrien DeLazzer Meunier, Jannik Gröne, Benjamin Haïoun, Alea Hofstetter, Theo Johnson-Freyd, David Jordan, Tessa Kammermeier, Patrick Kinnear, Cameron Krulewski, Theodoros Lagiotis, Leon Liu, Adrià Marín Salvador, Nivedita, David Reutter, Lorenzo Riva, Iordanis Romaidis, Jack Romo, Sean Sanford, Michail Tagaris, Daniel Teixeira, Jackson van Dyke, Matthias Vancraeynest, Chetan Vuppulury, Matthew Yu, Markus Zetto

arXiv ID: 2509.10636 | Date: 2025-09-12

Abstract: These lecture notes are the product of a week-long learning workshop on the work of Johnson-Freyd and Reutter on the problem of the existence of minimal nondegenerate extensions of braided fusion categories (arXiv:2105.15167). They recount the mathematical arguments of the original paper from an expository angle, with background material covering the algebra and homotopy theory required to understand the statement and follow the proof. The notes are aimed at newcomers to the field of (braided) fusion 1- and 2-categories.

Tunable Magnetic Order in Chiral Coupled Spin Chains

Authors: Rafael D. Soares, J. M. Viana Parente Lopes, Hugo Terças

arXiv ID: 2509.10286 | Date: 2025-09-12

Abstract: We obtain the ground-state phase diagram of two spin chains consisting in a set two-level systems asymmetrically coupled to an XX chain through a chiral interaction. The interaction is parametrized by its magnitude and an angle defined by the relative orientation of the spins in different chains. From the entanglement spectrum, we identify the critical lines separating distinct magnetically ordered phases, with the interaction angle able to shift or fully suppress the transition. By increasing the coupling strength, the systems is driven through a quantum phase transition, leading to the formation of two types of in-plane antiferromagnetic stripes. The interaction strength sets stripe formation, while the angle controls the spins orientations. The chiral interaction also induces a non-trivial finite vector spin chirality with opposite orientation on the chains. We show that the vector spin chirality emerges smoothly from the decoupled limit and occurs for angles different from zero and π/2π/2, where collinear order is favored instead.

Coarse-Grained BCFT Tensor Networks and Holographic Reflected Entropy in 3D Gravity

Authors: Ning Bao, Jinwei Chu, Yikun Jiang, Jacob March

arXiv ID: 2509.10170 | Date: 2025-09-12

Abstract: We use the framework of BCFT tensor networks\textit{BCFT tensor networks} to present a microscopic CFT derivation of the correspondence between reflected entropy (RE) and entanglement wedge cross section (EW) in AdS3_3/CFT2_2, for both bipartite and multipartite settings. These fixed-point tensor networks, obtained by triangulating Euclidean CFT path integrals, allow us to explicitly construct the canonical purification via cutting-and-gluing CFT path integrals. Employing modular flow in the large-cc limit, we demonstrate that these intrinsic CFT manipulations reproduce bulk geometric prescriptions, without assuming the AdS/CFT dictionary. The emergence of bulk geometry is traced to coarse-graining over heavy states in the large-cc limit. Universal coarse-grained BCFT data for compact 2D CFTs, through the relation to Liouville theory with ZZ boundary conditions, yields hyperbolic geometry on the Cauchy slice. The corresponding averaged replica partition functions reproduce all candidate EWs, arising from different averaging patterns, with the dominant one providing the correct RE and EW. In this way, many heuristic tensor-network intuitions in toy models are made precise and established directly from intrinsic CFT data.

The low-rank tensor-train finite difference method for three-dimensional parabolic equations

Authors: Gianmarco Manzini, Tommaso Sorgente

arXiv ID: 2509.10142 | Date: 2025-09-12

Abstract: This paper presents a numerical framework for the low-rank approximation of the solution to three-dimensional parabolic problems. The key contribution of this work is the tensorization process based on a tensor-train reformulation of the second-order accurate finite difference method. We advance the solution in time by combining the finite difference method with an explicit and implicit Euler method and with the Crank-Nicolson method. We solve the linear system arising at each time step from the implicit and semi-implicit time-marching schemes through a matrix-free preconditioned conjugate gradient (PCG) method, appositely designed to exploit the separation of variables induced by the tensor-train format. We assess the performance of our method through extensive numerical experimentation, demonstrating that the tensor-train design offers a robust and highly efficient alternative to the traditional approach. Indeed, the usage of this type of representation leads to massive time and memory savings while guaranteeing almost identical accuracy with respect to the traditional one. These features make the method particularly suitable to tackle challenging high-dimensional problems.

Entanglement architecture of beyond-Landau quantum criticality

Authors: Menghan Song, Ting-Tung Wang, Liuke Lyu, William Witczak-Krempa, Zi Yang Meng

arXiv ID: 2509.09983 | Date: 2025-09-12

Abstract: Quantum critical points beyond the Landau paradigm exhibit fractionalized excitations and emergent gauge fields. Here, we use entanglement microscopy--full tomography of the reduced density matrix of small subregions and subsequent extraction of their quantum correlations--to resolve the entanglement architecture near such exotic critical points. We focus on genuine multipartite entanglement (GME). Through unbiased quantum Monte Carlo sampling of RDMs across conventional O(2)/O(3) Wilson-Fisher transitions, and unconventional XY^*, and Néel-VBS transitions in (2+1)d, we discover a dichotomy: Landau criticality amplifies GME within compact subregions, while non-Landau criticality redistributes entanglement into larger, loopy configurations. Key signatures at non-Landau criticality include the absence of three-spin GME, and the loss of non-loopy entanglement in unicursal regions. Similar results in a critical resonating valence bond wavefunction confirm this multipartite entanglement structure as a common feature of emergent gauge theories. Our findings reveal a distinct entanglement architecture in beyond-Landau quantum critical theories.

PT symmetry-enriched non-unitary criticality

Authors: Kuang-Hung Chou, Xue-Jia Yu, Po-Yao Chang

arXiv ID: 2509.09587 | Date: 2025-09-11

Abstract: The interplay between topology and quantum criticality gives rise to the notion of symmetry-enriched criticality, which has attracted considerable attention in recent years. However, its non-Hermitian counterpart remains largely unexplored. In this Letter, we show how parity-time (PT) symmetry enriches non-Hermitian critical points, giving rise to a topologically distinct non-unitary universality class. By analytically investigating non-Hermitian free fermion models with PTPT symmetry, we uncover a new class of conformally invariant non-unitary critical points that host robust topological edge modes. Remarkably, the associated topological degeneracy is surprisingly encoded in the purely imaginary part of the entanglement entropy scaling-a feature absent in Hermitian systems. The underlying mechanism for the emergence of edge states at non-Hermitian criticality is traced to a generalized mass inversion that is absent in Hermitian systems.

Minimality of Tree Tensor Network Ranks

Authors: Jana Jovcheva, Tim Seynnaeve, Nick Vannieuwenhoven

arXiv ID: 2509.09463 | Date: 2025-09-11

Abstract: For a given tree tensor network GG, we call a tuple of bond dimensions minimal if there exists a tensor TT that can be represented by this network but not on the same tree topology with strictly smaller bond dimensions. We establish necessary and sufficient conditions on the bond dimensions of a tree tensor network to be minimal, generalizing a characterization of Carlini and Kleppe about existence of tensors with a given multilinear rank. We also show that in a minimal tree tensor network, the non-minimal tensors form a Zariski closed subset, so minimality is a generic property in this sense.

A Low-Rank tensor framework for THB-Splines

Authors: Tom-Christian Riemer, Martin Stoll

arXiv ID: 2509.09434 | Date: 2025-09-11

Abstract: We introduce a low-rank framework for adaptive isogeometric analysis with truncated hierarchical B-splines (THB-splines) that targets the main bottleneck of local refinement: memory- and time-intensive matrix assembly once the global tensor-product structure is lost. The method interpolates geometry-induced weight and source terms in separable spline spaces and computes their tensor-train (TT) representations via the alternating minimal energy (AMEn) solver, enabling level-wise assembly of system operators using univariate quadrature. To recover separability in the adaptive setting, we reduce the active basis to tensor-product domains and partition active/non-active cells into a small number of Cartesian cuboids, so each contributes a Kronecker factor that is accumulated and rounded in TT. We realize the two-scale relation with truncation in low rank and assemble the global hierarchical operators in a block TT format suitable for iterative solvers. A prototype MATLAB implementation built on the GeoPDEs package and the TT-Toolbox demonstrates that, for model problems with moderately complex refinement regions, the approach reduces memory footprint and assembly time while maintaining accuracy; we also discuss limitations when ranks grow with geometric or refinement complexity. This framework advances scalable adaptive IgA with THB-splines, particularly in three dimensions.

Matrix product state classification of 1D multipole symmetry protected topological phases

Authors: Takuma Saito, Weiguang Cao, Bo Han, Hiromi Ebisu

arXiv ID: 2509.09244 | Date: 2025-09-11

Abstract: Spatially modulated symmetries are one of the new types of symmetries whose symmetry actions are position dependent. Yet exotic phases resulting from these spatially modulated symmetries are not fully understood and classified. In this work, we systematically classify one dimensional bosonic symmetry protected topological phases protected respecting multipole symmetries by employing matrix product state formalism. The symmetry action induces projective representations at the ends of an open chain, which we identify via group cohomology. In particular, for rr-pole symmetries, for instance, rr = 0 (global), 1 (dipole), and 2 (quadrupole), the classification is determined by distinct components of second cohomology groups that encode the boundary projective representations.

Bosonic realization of SU(3) chiral Haldane phases

Authors: Linpu Zhang, Junjun Xu

arXiv ID: 2509.09083 | Date: 2025-09-11

Abstract: We give a bosonic realization of the SU(3) antiferromagnetic Heisenberg (AFH) chain in the alternating conjugate representation, and study its phase diagram as a function of staggered interactions and anisotropy along the T3T^3 and T8T^8 directions. Unlike the SU(2) case, we observe a chiral-reversed quantum phase transition, where each competing phase is adiabatically connected to one of the chiral Haldane phases predicted in the SU(3) AFH chain with local adjoint representation. In the vicinity of the Heisenberg point, we identify a symmetry-protected topological state that appears at the first excited energy level. We also study the spontaneous Z3\mathbb{Z}_3 symmetry breaking of the system, and provide a variational wavefunction that captures the transition from the topological phase to the trivial phase. Finally, we propose an experimental realization of our bosonic model by two spin-1/2 bosons in an optical lattice.

Demystifying quantum escapism on the honeycomb lattice

Authors: A. L. Chernyshev

arXiv ID: 2509.08877 | Date: 2025-09-10

Abstract: We demonstrate the versatility, simplicity, and power of the minimally-augmented spin-wave theory in studying phase diagrams of the quantum spin models in which unexpected magnetically ordered phases occur or the existing ones expand beyond their classical stability regions. We use this method to obtain approximate phase diagrams of the two paradigmatic spin-12\frac{1}{2} models on the honeycomb lattice: the J1J_1-J3J_3 ferro-antiferromagnetic and J1J_1-J2J_2 antiferromagnetic XXZXXZ models. For the J1J_1-J3J_3 case, various combinations of the XXZXXZ anisotropies are analyzed. In a dramatic deviation from their classical phase diagrams, which host significant regions of the noncollinear spiral phases, quantum fluctuations stabilize several unconventional collinear phases and significantly extend conventional ones to completely supersede spiral states. These results are in close agreement with the available density-matrix renormalization group calculations. The applicability of this approach to the other models and its potential extension to different types of orders are discussed.

Kitaev-derived Gapless Spin Liquid in the KK-JJ-ΓΓ-ΓΓ' Quantum Magnet Na2_2Co2_2TeO6_6

Authors: Han Li, Xu-Guang Zhou, Gang Su, Wei Li

arXiv ID: 2509.08821 | Date: 2025-09-10

Abstract: The realization of quantum spin liquids (QSLs) in Kitaev magnets represents an intriguing topic in frustrated quantum magnetism. Despite prediction in the pure Kitaev honeycomb model, realization of QSLs in realistic systems and materials remain scarce. The recent discovery of cobalt-based compound Na2_2Co2_2TeO6_6 has raised significant research interest. By establishing a realistic KK-JJ-ΓΓ-ΓΓ' model for Na2_2Co2_2TeO6_6 -- with a dominant antiferromagnetic (AFM) Kitaev interaction (K>0K>0) that quantitatively explains its thermodynamics measurements -- we reveal an intermediate gapless QSL phase under [111] magnetic fields with tensor-network calculations. We confirm the QSL nature of this phase by demonstrating its adiabatic connection to the intensively studied intermediate QSL of the pure AFM Kitaev model under out-of-plane fields. Our results show excellent agreement with recent high-field experiments, thereby explaining the intermediate-field phase in Na2_2Co2_2TeO6_6. These findings bridge the gap between theoretical proposals for a Kitaev-derived QSL and experimental realization, opening new avenues for exploring exotic quantum states of matter in realistic Kitaev materials.

Real-Time String Dynamics in a 2+12+1D Non-Abelian Lattice Gauge Theory: String Breaking, Glueball Formation, Baryon Blockade, and Tension Reduction

Authors: Giovanni Cataldi, Simone Orlando, Jad C. Halimeh

arXiv ID: 2509.08868 | Date: 2025-09-10

Abstract: Understanding flux string dynamics can provide insight into quark confinement and hadronization. First-principles quantum and numerical simulations have mostly focused on toy-model Abelian lattice gauge theories (LGTs). With the advent of state-of-the-art quantum simulation experiments, it is important to bridge this gap and study string dynamics in non-Abelian LGTs beyond one spatial dimension. Using tensor network methods, we simulate the real-time string dynamics of a 2 ⁣+ ⁣12\!+\!1D SU(2)(2) Yang--Mills LGT with dynamical matter. In the strong-coupling regime and at resonance, string breaking occurs through sharp Casimir reduction along with meson and baryon-antibaryon formation, a distinctively non-Abelian feature. At finite baryon density, we discover a \textit{baryon blockade} mechanism that delays string breaking. Away from resonance, the magnetic term drives purely non-Abelian fluctuations: glueball loops and self-crossed strings that resolve two SU(2)(2) intertwiners with distinct dynamics. For higher-energy strings, we uncover representation-dependent tension-reduction resonances. Our findings serve as a guide for upcoming quantum simulators of non-Abelian LGTs.

Tensor-Train Operator Inference

Authors: Engin Danis, Duc Truong, Kim Ø. Rasmussen§, Boian S. Alexandrov

arXiv ID: 2509.08071 | Date: 2025-09-09

Abstract: In this study, we present a tensor--train framework for nonintrusive operator inference aimed at learning discrete operators and using them to predict solutions of physical governing equations. Our framework comprises three approaches: full--order tensor--train operator inference, full--order quantized tensor--train operator inference, and reduced--order tensor--train operator inference. In each case, snapshot data is represented in tensor--train format--either through compression or cross interpolation--enabling the efficient handling of extremely large datasets with significantly reduced computational effort compared to standard methods. The effectiveness of each approach is demonstrated through numerical experiments related to Computational Fluid Dynamics and benchmarked against the standard reduced--order operator inference method, highlighting the advantages of the tensor--train representations in both accuracy and scalability.

Resource complexity of Symmetry Protected Topological phases

Authors: Alberto Giuseppe Catalano, Sven Benjamin Kožić, Gianpaolo Torre, Carola Ciaramelletti, Simone Paganelli, Fabio Franchini, Salvatore Marco Giampaolo

arXiv ID: 2509.08053 | Date: 2025-09-09

Abstract: We pursue the identification of quantum resources carried by topological order, by evaluating quantum magic, quantified through the rank-22 Stabilizer Rényi entropy M2\mathcal{M}_2, in one-dimensional systems hosting symmetry-protected topological phases (SPTP). Focusing on models with an exact duality between an SPTP and a trivial one, namely the dimerized XX and the Cluster-Ising chains, we show that dual points exhibit identical amounts of magic, even thought they belong to distinct topological sectors. A subextensive asymmetry arises only under open boundary conditions, where edge effects break the duality, but this correction is non-topological and depends on microscopic parameters. These results stand in contrast to the case of topological frustration, where delocalized excitations enhance the magic logarithmically with system size. They also complement recent analyses in the literature, showing that the total magic is largely insensitive to the presence of topological order, hence suggesting that topological order is not necessarily a genuine computational resource.

Customizing the Inductive Biases of Softmax Attention using Structured Matrices

Authors: Yilun Kuang, Noah Amsel, Sanae Lotfi, Shikai Qiu, Andres Potapczynski, Andrew Gordon Wilson

arXiv ID: 2509.07963 | Date: 2025-09-09

Abstract: The core component of attention is the scoring function, which transforms the inputs into low-dimensional queries and keys and takes the dot product of each pair. While the low-dimensional projection improves efficiency, it causes information loss for certain tasks that have intrinsically high-dimensional inputs. Additionally, attention uses the same scoring function for all input pairs, without imposing a distance-dependent compute bias for neighboring tokens in the sequence. In this work, we address these shortcomings by proposing new scoring functions based on computationally efficient structured matrices with high ranks, including Block Tensor-Train (BTT) and Multi-Level Low Rank (MLR) matrices. On in-context regression tasks with high-dimensional inputs, our proposed scoring functions outperform standard attention for any fixed compute budget. On language modeling, a task that exhibits locality patterns, our MLR-based attention method achieves improved scaling laws compared to both standard attention and variants of sliding window attention. Additionally, we show that both BTT and MLR fall under a broader family of efficient structured matrices capable of encoding either full-rank or distance-dependent compute biases, thereby addressing significant shortcomings of standard attention. Finally, we show that MLR attention has promising results for long-range time-series forecasting.

A Tensor Network Framework for Lindbladian Spectra and Steady States

Authors: Philipp Westhoff, Mattia Moroder, Ulrich Schollwöck, Sebastian Paeckel

arXiv ID: 2509.07709 | Date: 2025-09-09

Abstract: Quantum systems coupled to (non-)Markovian environments attract increasing attention due to their peculiar physical properties. Exciting prospects such as unconventional non-equilibrium phases beyond the Mermin-Wagner limit, or the environment-assisted, robust preparation of highly entangled states, demand a systematic analysis of quantum many-body phases out of equilibrium. Akin to the equilibrium case, this requires the computation of the low-lying eigenstates of Lindbladians, a problem challenging conventional approaches for simulating quantum many-body systems. Here, we undertake a first step to overcome this limitation and introduce a tensor-network-based framework to compute systematically not only steady states, but also low-lying excited states with unprecedented precision for large, driven quantum many-body systems. Our framework is based on recent advances utilizing complex-time Krylov spaces, and we leverage these ideas to create a toolbox tailored to solve the challenging non-Hermitian eigenvalue problem ubiquitous in open quantum systems. At the example of the interacting Bose-Hubbard model driven by dissipation-assisted hopping, we demonstrate the high efficiency and accuracy, enabling us to perform a reliable finite-size scaling analysis of the spectral gap and demonstrating the existence of anomalous relaxation. This method unlocks the capability of spectral analysis of generic open quantum many-body systems, suitable also for non-Markovian environments.

Process Tensor Approaches to Non-Markovian Quantum Dynamics

Authors: Jonathan Keeling, E. Miles Stoudenmire, Mari-Carmen Bañuls, David R. Reichman

arXiv ID: 2509.07661 | Date: 2025-09-09

Abstract: The paradigm of considering open quantum systems -- i.e. focusing only on the system of interest, and treating the rest of the world as an effective environment -- has proven to be a highly effective way to understand a range of quantum systems, across areas of study such as quantum optics, cold atoms, superconducting qubits, and impurities in solid-state systems. A common approach in many of these contexts has been to consider simplified approaches based on the Born and Markov approximations. While these approximations are indeed often appropriate in contexts such as quantum optics, the widespread application of these approximations has been driven more by simplicity than by accuracy. In particular, these Markovian treatments will fail in many cases, such as when coupling to the environment is not weak, when the environment is structured and has resonances, when the system couples to low-frequency modes of the environment, or when the questions of interest involve the propagation of information through the environment. Despite the fact that many real problems are non-Markovian, the Markov approximation is still widely used, as it is often assumed that a fully non-Markovian treatment is too complex to be practical. In this perspective we discuss a recently developed set of techniques that address this challenge. Centering our discussion around the notion of the process tensor, we demonstrate that the generality of the process tensor concept, coupled with efficient tensor-network methods, opens the door to the description of a wide range of observable non-Markovian processes in a wide range of open quantum systems.

Large-scale Efficient Molecule Geometry Optimization with Hybrid Quantum-Classical Computing

Authors: Yajie Hao, Qiming Ding, Xiaoting Wang, Xiao Yuan

arXiv ID: 2509.07460 | Date: 2025-09-09

Abstract: Accurately and efficiently predicting the equilibrium geometries of large molecules remains a central challenge in quantum computational chemistry, even with hybrid quantum-classical algorithms. Two major obstacles hinder progress: the large number of qubits required and the prohibitive cost of conventional nested optimization. In this work, we introduce a co-optimization framework that combines Density Matrix Embedding Theory (DMET) with Variational Quantum Eigensolver (VQE) to address these limitations. This approach substantially reduces the required quantum resources, enabling the treatment of molecular systems significantly larger than previously feasible. We first validate our framework on benchmark systems, such as H4 and H2O2, before demonstrating its efficacy in determining the equilibrium geometry of glycolic acid C2H4O3, a molecule of a size previously considered intractable for quantum geometry optimization. Our results show the method achieves high accuracy while drastically lowering computational cost. This work thus represents a significant step toward practical, scalable quantum simulations, moving beyond the small, proof-of-concept molecules that have historically dominated the field. More broadly, our framework establishes a tangible path toward leveraging quantum advantage for the in silico design of complex catalysts and pharmaceuticals.

Time evolution of controlled many-body quantum systems with matrix product operators

Authors: Llorenç Balada Gaggioli, Jakub Mareček

arXiv ID: 2509.07228 | Date: 2025-09-08

Abstract: We present a method for describing the time evolution of many-body controlled quantum systems using matrix product operators (MPOs). Existing techniques for solving the time-dependent Schrödinger equation (TDSE) with an MPO Hamiltonian often rely on time discretization. In contrast, our approach uses the Magnus expansion and Chebyshev polynomials to model the time evolution, and the MPO representation to efficiently encode the system's dynamics. This results in a scalable method that can be used efficiently for many-body controlled quantum systems. We apply this technique to quantum optimal control, specifically for a gate synthesis problem, demonstrating that it can be used for large-scale optimization problems that are otherwise impractical to formulate in a dense matrix representation.

Tensor Network based Gene Regulatory Network Inference for Single-Cell Transcriptomic Data

Authors: Olatz Sanz Larrarte, Borja Aizpurua, Reza Dastbasteh, Ruben M. Otxoa, Josu Etxezarreta Martinez

arXiv ID: 2509.06891 | Date: 2025-09-08

Abstract: Deciphering complex gene-gene interactions remains challenging in transcriptomics as traditional methods often miss higher-order and nonlinear dependencies. This study introduces a quantum-inspired framework leveraging tensor networks (TNs) to optimally map expression data into a lower dimensional representation preserving biological locality. Using Quantum Mutual Information (QMI), a nonparametric measure natural for tensor networks, we quantify gene dependencies and establish statistical significance via permutation testing. This constructs robust interaction networks where the edges reflect biologically meaningful relationships that are resilient to random chance. The approach effectively distinguishes true regulatory patterns from experimental noise and biological stochasticity. To test the proposed method, we recover a gene regulatory network consisted of six pathway genes from single-cell RNA sequencing data comprising over 28.00028.000 lymphoblastoid cells. Furthermore, we unveil several triadic regulatory mechanisms. By merging quantum physics inspired techniques with computational biology, our method provides novel insights into gene regulation, with applications in disease mechanisms and precision medicine.

Confinement, deconfinement, and bound states in the spin-11 and spin-3/23/2 generalizations of the Majumdar--Ghosh chain

Authors: Aman Sharma, Mithilesh Nayak, Natalia Chepiga, Henrik M. Rønnow, Frédéric Mila

arXiv ID: 2509.06720 | Date: 2025-09-08

Abstract: We investigate the nature of low-energy excitations in a spin chain with antiferrmomagnetic nearest-neighbor J1J_1, next-nearest-neighbor J2J_2, and three-site J3J_3 interactions using the time-dependent density matrix renormalization group and the single mode approximation techniques. In the absence of the J2J_2 interaction, we identify clear distinctions in the spectral functions in the fully dimerized phase across the exactly dimerized line for different magnitudes of the spins. In contrast to the spin-1/21/2 chain, where the spinon continuum dominates the spectral functions, the magnon modes are prominent in the spectral functions of the spin-11 and spin-3/23/2 chains. Through single mode approximation and valence bond solid approaches, we disentangle magnon and spinon contributions to the spectral functions. After including the J2J_2 interactions, for the spin-11 chain we trace the evolution of the dynamical structure factor along the phase transition line between the Haldane phase and the fully dimerized phase. We find that the excitation spectrum is a continuum along this line and the spectral gap closes as the order of the transition changes from first order to second order. Along the line of first-order transitions, the spinon-like domain walls are deconfined, and the model exhibits their confinement into discrete bound states away from the transition line. A similar phenomenon occurs in the spin-3/23/2 chain across the phase transition between partially dimerized to fully dimerized phases, revealing a universal spinon confinement phenomenon across first-order phase transitions. This study presents the dynamical structure factor corresponding to the ground state phase diagram and establishes a unified quasiparticle framework for understanding the fundamental nature of excitations across distinct quantum phases in frustrated J1J_1-J2J_2-J3J_3 Heisenberg spin chains.

Classical Neural Networks on Quantum Devices via Tensor Network Disentanglers: A Case Study in Image Classification

Authors: Borja Aizpurua, Sukhbinder Singh, Román Orús

arXiv ID: 2509.06653 | Date: 2025-09-08

Abstract: We address the problem of implementing bottleneck layers from classical pre-trained neural networks on a quantum computer, with the goal of achieving quantum advantage on near-term devices. Our approach begins with a compression step in which the target linear layer is represented as an effective matrix product operator (MPO) without degrading model performance. The MPO is then further disentangled into a more compact form. This enables a hybrid classical-quantum execution scheme, where the disentangling circuits are deployed on a quantum computer while the remainder of the network -- including the disentangled MPO -- runs on classical hardware. We introduce two complementary algorithms for MPO disentangling: (i) an explicitly disentangling variational method leveraging standard tensor-network optimization techniques, and (ii) an implicitly disentangling gradient-descent-based approach. We validate these methods through a proof-of-concept translation of simple classical neural networks for MNIST and CIFAR-10 image classification into a hybrid classical-quantum form.

Site Basis Excitation Ansatz for Matrix Product States

Authors: Steven R. White

arXiv ID: 2509.06241 | Date: 2025-09-07

Abstract: We introduce a simple and efficient variation of the tangent-space excitation ansatz used to compute elementary excitation spectra of one-dimensional quantum lattice systems using matrix product states (MPS). A small basis for the excitation tensors is formed based on a single diagonalization analogous to a single site DMRG step but for multiple states. Once overlap and Hamiltonian matrix elements are found, obtaining the excitation for any momentum only requires diagonalization of a tiny matrix, akin to a non-orthogonal band-theory diagonalization. The approach is based on an infinite MPS description of the ground state, and we introduce an extremely simple alternative to variational uniform matrix product states (VUMPS) based on finite system DMRG. For the S=1S=1 Heisenberg chain, our method -- site basis excitation ansatz (SBEA) -- efficiently produces the one-magnon dispersion with high accuracy. We also examine the role of MPS gauge choices, finding that not imposing a gauge condition -- leaving the basis nonorthogonal -- is crucial for the approach, whereas imposing a left-orthonormal gauge (as in prior work) severely hampers convergence. We also show how one can construct Wannier excitations, analogous to the Wannier functions of band theory, where one Wannier excitation, translated to all sites, can reconstruct the single magnon modes exactly for all momenta.

Efficient iPEPS Simulation on the Honeycomb Lattice via QR-based CTMRG

Authors: Qi Yang, Philippe Corboz

arXiv ID: 2509.05090 | Date: 2025-09-05

Abstract: We develop a QR-based corner transfer matrix renormalization group (CTMRG) framework for contracting infinite projected entangled-pair states (iPEPS) on honeycomb lattices. Our method explicitly uses the lattice's native C3v symmetry at each site, generalizing QR-based acceleration (previously limited to square lattices) to enable efficient and stable contractions. This approach achieves order-of-magnitude speedups over conventional singular value decomposition (SVD)-based CTMRG while maintaining high numerical precision. Comprehensive benchmark calculations for the spin-1/2 Heisenberg and Kitaev models demonstrate higher computational efficiency without sacrificing accuracy. We further employ our method to study the Kitaev-Heisenberg model, where we provide numerical evidence for the universal 1/r^4 decay of the dimer-dimer correlation function within the quantum spin liquid (QSL) phase. Our work establishes a framework for extending QR-based CTMRG to other lattice geometries, opening new avenues for studying exotic quantum phases with tensor networks.

Note on searching for critical lattice models as entropy critical points from strange correlator

Authors: Anran Jin, Ling-Yan Hung

arXiv ID: 2509.04947 | Date: 2025-09-05

Abstract: An entropy function is proposed in [Phys. Rev. Lett. 131, 251602] as a way to detect criticality even when the system size is small. In this note we apply this strategy in the search for criticality of lattice transfer matrices constructed based on the topological holographic principle. We find that the combination of strategy is indeed a cost-effective and efficient way of identifying critical boundary conditions, estimating central charges and moreover, plotting entire phase diagrams in a multi-dimensional phase space.

A systematic search for conformal field theories in very small spaces

Authors: Xiang Li, Ting-Chun Lin, John McGreevy

arXiv ID: 2509.04596 | Date: 2025-09-04

Abstract: Groundstates of 1+1d conformal field theories (CFTs) satisfy a local entropic condition called the vector fixed point equation. This condition is surprisingly well satisfied by groundstates of quantum critical lattice models even at small system sizes. We perform a search in the space of states of very small systems (four qubits and four qutrits) and examine the states that satisfy this condition. By reconstructing a local Hamiltonian from each state, we are able to identify many of these solutions with known CFTs; others are gapped fixed points, or involve large relevant perturbations, and others are CFTs we have not yet identified. These ideas are also useful for identifying continuous quantum phase transitions in a given family of Hamiltonians, and for identifying the nature of the critical theory in small systems.

Symmetric entanglers for non-invertible SPT phases

Authors: Minyoung You

arXiv ID: 2509.04581 | Date: 2025-09-04

Abstract: It has been suggested that non-invertible symmetry protected topological phases (SPT), due to the lack of a stacking structure, do not have symmetric entanglers (globally symmetric finite-depth quantum circuits) connecting them. Using topological holography, we argue that a symmetric entangler should in fact exist for 1+11+1d systems whenever the non-invertible symmetry has SPT phases connected by fixed-charge dualities (FCD). Moreover, we construct an explicit example of a symmetric entangler for the two SPT phases with Rep(A4)\mathrm{Rep}(A_4)-symmetry, as a matrix product unitary (MPU).

Low-rank matrix and tensor approximations: advancing efficiency of machine-learning interatomic potentials

Authors: Igor Vorotnikov, Fedor Romashov, Nikita Rybin, Maxim Rakhuba, Ivan S. Novikov

arXiv ID: 2509.04440 | Date: 2025-09-04

Abstract: Machine-learning interatomic potentials (MLIPs) have become a mainstay in computationally-guided materials science, surpassing traditional force fields due to their flexible functional form and superior accuracy in reproducing physical properties of materials. This flexibility is achieved through mathematically-rigorous basis sets that describe interatomic interactions within a local atomic environment. The number of parameters in these basis sets influences both the size of the training dataset required and the computational speed of the MLIP. Consequently, compressing MLIPs by reducing the number of parameters is a promising route to more efficient simulations. In this work, we use low-rank matrix and tensor factorizations under fixed-rank constraints to achieve this compression. In addition, we demonstrate that an algorithm with automatic rank augmentation helps to find a deeper local minimum of the fitted potential. The methodology is verified using the Moment Tensor Potential (MTP) model and benchmarked on multi-component systems: a Mo-Nb-Ta-W medium-entropy alloy, molten LiF-NaF-KF, and a glycine molecular crystal. The proposed approach achieves up to 50% compression without any loss of MTP accuracy and can be applied to compress other MLIPs.

Infinite temperature at zero energy

Authors: Matteo Ippoliti, David M. Long

arXiv ID: 2509.04410 | Date: 2025-09-04

Abstract: We construct a family of static, geometrically local Hamiltonians that inherit eigenstate properties of periodically-driven (Floquet) systems. Our construction is a variation of the Feynman-Kitaev clock -- a well-known mapping between quantum circuits and local Hamiltonians -- where the clock register is given periodic boundary conditions. Assuming the eigenstate thermalization hypothesis (ETH) holds for the input circuit, our construction yields Hamiltonians whose eigenstates have properties characteristic of infinite temperature, like volume-law entanglement entropy, across the whole spectrum -- including the ground state. We then construct a family of exactly solvable Floquet quantum circuits whose eigenstates are shown to obey the ETH at infinite temperature. Combining the two constructions yields a new family of local Hamiltonians with provably volume-law-entangled ground states, and the first such construction where the volume law holds for all contiguous subsystems.

Excitonic description of singlet fission beyond dimer model : a matrix product state approach

Authors: Supriyo Santra, Amartya Bose, Debashree Ghosh

arXiv ID: 2509.03966 | Date: 2025-09-04

Abstract: The importance of singlet fission as a fundamental process with a variety of implications in energy harvesting cannot be overstated. The challenge is in characterizing the energy states of these large singlet fission molecular aggregates that participate in the process. Large dimensionality and essential multi-configuration nature of the electronic states of interest combine to make accurate ab initio calculations prohibitively difficult. We present a spin-resolved tight-binding excitonic model for singlet fission that can be parameterized based on ab initio calculations on monomers and dimers of molecules, and is highly suitable for the study of aggregates using tensor network methods such as the density matrix renormalization group. This tensor network coarse-grained model is demonstrated specifically on the pentacene crystal, where we evaluate the spectra and density of states. We show the natural emergence of bands of states in some cases, and characterize them. Through an analysis of entanglement entropy of the eigenstates, we gain crucial insight into the extent of their multireference character. This method is useful in understanding not just the structure of these extended aggregates, but also being the cornerstone for incorporation of vibronic features and simulation of the singlet fission dynamics.

The ITransverse.jl library for transverse tensor network contractions

Authors: Stefano Carignano

arXiv ID: 2509.03699 | Date: 2025-09-03

Abstract: Transverse contraction methods are extremely promising tools for the efficient contraction of tensor networks associated with the time evolution of quantum many-body systems, allowing in some cases to circumvent the entanglement barrier that would normally prevent the study of quantum dynamics with classical resources. We present here the ITransverse.jl package, written in Julia and based on ITensors.jl, containing several of these high-level algorithms, including novel prescriptions for efficient truncations of temporal matrix product states.

Trading Mathematical for Physical Simplicity: Bialgebraic Structures in Matrix Product Operator Symmetries

Authors: Yuhan Liu, Andras Molnar, Xiao-Qi Sun, Frank Verstraete, Kohtaro Kato, Laurens Lootens

arXiv ID: 2509.03600 | Date: 2025-09-03

Abstract: Despite recent advances in the lattice representation theory of (generalized) symmetries, many simple quantum spin chains of physical interest are not included in the rigid framework of fusion categories and weak Hopf algebras. We demonstrate that this problem can be overcome by relaxing the requirements on the underlying algebraic structure, and show that general matrix product operator symmetries are described by a pre-bialgebra. As a guiding example, we focus on the anomalous Z2\mathbb Z_2 symmetry of the XX model, which manifests the mixed anomaly between its U(1)U(1) momentum and winding symmetry. We show how this anomaly is embedded into the non-semisimple corepresentation category, providing a novel mechanism for realizing such anomalous symmetries on the lattice. Additionally, the representation category which describes the renormalization properties is semisimple and semi-monoidal, which provides a new class of mixed state renormalization fixed points. Finally, we show that up to a quantum channel, this anomalous Z2\mathbb Z_2 symmetry is equivalent to a more conventional MPO symmetry obtained on the boundary of a double semion model. In this way, our work provides a bridge between well-understood topological defect symmetries and those that arise in more realistic models.

A new rung on the ladder: exploring topological frustration towards two dimensions

Authors: Alberto Giuseppe Catalano, Nora Reinić, Gianpaolo Torre, Sven Benjamin Kožić, Karlo Delić, Simone Montangero, Fabio Franchini, Salvatore Marco Giampaolo

arXiv ID: 2509.03574 | Date: 2025-09-03

Abstract: Topological frustration arises when boundary conditions impose geometric frustration in a quantum system, creating delocalized defects in the ground states and profoundly altering the low-energy properties. While previous studies have been concerned with one-dimensional systems, showing that the ground state structure can be described in terms of quasiparticle excitations, the two-dimensional setting remains unexplored. We address this gap by studying a three-legged antiferromagnetic quantum Ising ladder on a torus using tensor network methods, where topological frustration is induced by an odd number of spins along both spatial directions. Our results reveal the first instance in which topological frustration shifts the position of the quantum critical point. By studying the entanglement structure, we find that the ground state can be characterized as hosting three delocalized quasiparticles. This work builds the quasiparticle picture of topological frustration toward higher dimensions and more complex systems than those considered so far.

Dissipationless dynamics of spin supersolid states in a spin-1/2 triangular antiferromagnet with impurities

Authors: Yixuan Huang, Yuan Gao, Wei Li, Seiji Yunoki, Sadamichi Maekawa

arXiv ID: 2509.03489 | Date: 2025-09-03

Abstract: Motivated by recent experimental observations of the possible spin supersolid states in triangular lattice compounds, we study the dynamical properties of various ground states in the spin-1/2 easy-axis antiferromagnetic Heisenberg model with impurities under magnetic fields using numerical methods. In both low- and high-field spin supersolid states, the gapless Goldstone mode at the KK points remains robust against impurities, which is related to the presence of spin superfluidity. By contrast, we find that impurities induce a splitting of the magnon bands at the same density level in the conventional magnetic state, the so-called up-up-down state. In addition, the finite superfluid stiffness probed by the twisted phase in the spin supersolid states is consistent with the excitation spectrum. We argue that this excitation spectrum with impurity provides direct evidence for the dissipationless dynamics in the spin supersolid states, which could be tested in neutron scattering experiments.

Universal representation of the long-range entanglement in the family of Toric Code states

Authors: Mohammad Hossein Zarei, Mohsen Rahmani Haghighi

arXiv ID: 2509.03422 | Date: 2025-09-03

Abstract: Since the long range entanglement is a universal characteristic of topological quantum states belonging to the same class, a suitable mathematical representation of the long range entanglement has to be also universal. In this Letter, we introduce such a representation for the family of Toric Code states by using Kitaev's Ladders as building blocks. We consider Toric Code states corresponding to various planar graphs and apply non-local dientanglers to qubits corresponding to non-contractible cycles that satisfy a topological constraint. We demonstrate that, independent of the geometry of the underlying graph, disentanglers convert Toric Code states into a tensor product of Kitaev's Ladder states. Since Kitaev's Ladders with arbitrary geometric configurations include the short-range entanglements, we conclude that the above universal and non-local pattern of entanglement between ladders is responsible of the long-range entanglement inherent in Toric Code states. Our result emphasizes in the capability of such non-local representations to describe topological order in ground-state wave functions of topological quantum systems.

Topology meets superconductivity in a one-dimensional tJt-J model of magnetic atoms

Authors: Leonardo Bellinato Giacomelli, Thomas Bland, Louis Lafforgue, Francesca Ferlaino, Manfred J. Mark, Luca Barbiero

arXiv ID: 2509.03387 | Date: 2025-09-03

Abstract: Strongly interacting fermions represent the key constituent of several intriguing phases of matter. However, due to the inherent complexity of these systems, important regimes are still inaccessible. Here, we derive a realistic and flexible setup based on ultracold magnetic lanthanide atoms trapped in a one-dimensional optical lattice. Leveraging their large magnetic moments, we design a fermionic tJt-J model with independently tunable hopping, spin-spin couplings, and onsite interaction. Through combined analytical and numerical analysis, we uncover a variety of many-body quantum phases-including superconducting and topological states. Crucially, in the regime of attractive onsite interaction we reveal that topology and superconductivity coexist, thus giving rise to an exotic state of matter: a topological triplet superconductor. We also outline a practical protocol to prepare and detect all discovered phases using current experimental techniques. Our results establish an alternative and powerful route for a deeper understanding of strongly interacting fermionic quantum matter.

TeRA: Vector-based Random Tensor Network for High-Rank Adaptation of Large Language Models

Authors: Yuxuan Gu, Wuyang Zhou, Giorgos Iacovides, Danilo Mandic

arXiv ID: 2509.03234 | Date: 2025-09-03

Abstract: Parameter-Efficient Fine-Tuning (PEFT) methods, such as Low-Rank Adaptation (LoRA), have significantly reduced the number of trainable parameters needed in fine-tuning large language models (LLMs). Subsequent developments of LoRA-style adapters have diverged into two main directions: (1) enhancing model expressivity with high-rank adapters, and (2) pushing for further parameter reduction, as exemplified by vector-based methods. However, these approaches present a trade-off, as achieving the expressivity of high-rank weight updates typically comes at the cost of sacrificing the extreme parameter efficiency offered by vector-based techniques. To address this issue, we propose a vector-based random \underline{\textbf{Te}}nsor network for high-\underline{\textbf{R}}ank \underline{\textbf{A}}daptation (TeRA), a novel PEFT method that achieves high-rank weight updates while retaining the parameter efficiency of vector-based PEFT adapters. This is achieved by parameterizing the tensorized weight update matrix as a Tucker-like tensor network (TN), in which large randomly initialized factors are frozen and shared across layers, while only small layer-specific scaling vectors, formed by entries in diagonal factor matrices, are trained. This design effectively decouples the rank of the weight update matrix from the number of trainable parameters. Comprehensive experiments demonstrate that TeRA matches or even outperforms high-rank adapters, while requiring a trainable parameter count similar to vector-based methods. Theoretical analysis and ablation studies further validate the effectiveness of our approach.

Deconfined Quantum Critical Point in Quantum Hall Bilayers

Authors: Guangyu Yu, Tao Xiang, Zheng Zhu

arXiv ID: 2509.03079 | Date: 2025-09-03

Abstract: Deconfined quantum critical points (DQCPs) represent an unconventional class of quantum criticality beyond the Landau-Ginzburg-Wilson-Fisher paradigm. Nevertheless, both their theoretical identification and experimental realization remain challenging. Here we report compelling evidence of a DQCP in quantum Hall bilayers with half-filled n=2n=2 Landau levels in each layer, based on large-scale variational uniform matrix product state (VUMPS) simulations and exact diagonalization (ED). By systematically analyzing the ground-state fidelity, low-lying energy spectra, exciton superfluid and stripe order parameters, and ground-state energy derivatives, we identify a direct and continuous quantum phase transition between two distinct symmetry-breaking phases by tuning the layer separation: an exciton superfluid phase with spontaneous U(1)U(1) symmetry breaking at small separation, and a unidirectional charge density wave with broken translational symmetry at large separation. Our results highlight quantum Hall bilayers as an ideal platform for realizing and experimentally probing DQCPs under precisely tunable interactions.

Topological Chiral Superconductivity in the Triangular-Lattice Hofstadter-Hubbard Model

Authors: Feng Chen, Wen O. Wang, Jia-Xin Zhang, Leon Balents, D. N. Sheng

arXiv ID: 2509.02757 | Date: 2025-09-02

Abstract: Moiré materials provide exciting platforms for studying the interplay of strong electronic correlation and large magnetic flux effects. We study the lightly doped Hofstadter-Hubbard model on a triangular lattice through large-scale density matrix renormalization group and determinantal quantum Monte Carlo simulations. We find strong evidence for a robust chiral superconducting (SC) phase with dominant power-law pairing correlations and a quantized spin Chern number. The SC phase emerges at very weak interaction and grows stronger at intermediate interaction strengths (U ) for a wide range of hole doping. We also discuss the possible distinct nature of the normal state in different U regimes. Our work provides theoretical insights into the emergence of topological superconductivity from doping topological Chern bands or magnetic flux induced chiral spin liquid states of Moiré materials.

Scattering and induced false vacuum decay in the two-dimensional quantum Ising model

Authors: Luka Pavešić, Marco Di Liberto, Simone Montangero

arXiv ID: 2509.02702 | Date: 2025-09-02

Abstract: We study scattering in the quantum Ising model in two dimensions. In the ordered phase, the spectrum contains a ladder of bound states and intertwined scattering resonances, which enable various scattering channels. By preparing wave packets on a 24×2424 \times 24 lattice and evolving the state with tensor networks, we explore and characterize these regimes, ranging from elastic scattering in the perturbative regime, to non-perturbative processes closer to the critical point. Then, we break the spin inversion symmetry and study the stability of the metastable false vacuum state on the collision of its excitations. We find that a highly-energetic scattering process can induce a violent decay of the false vacuum, and investigate the spread of the resulting true vacuum bubble.

Robust superconductivity upon doping chiral spin liquid and Chern insulators in a Hubbard-Hofstadter model

Authors: Clemens Kuhlenkamp, Stefan Divic, Michael P. Zaletel, Tomohiro Soejima, Ashvin Vishwanath

arXiv ID: 2509.02675 | Date: 2025-09-02

Abstract: Demonstrating superconductivity in purely repulsive Hubbard models is a compelling goal which underscores the counter-intuitive ability of Coulomb interactions to mediate superconductivity. Here, we present numerical evidence for robust superconductivity in a triangular Hubbard-Hofstadter model at π/2π/2 flux per plaquette. Employing infinite density matrix renormalization group calculations on infinite cylinders of finite circumference, we observe superconducting ground states for a wide range of dopings, whose pair-correlations strengthen as the 2D limit is approached. At a density of one electron per site, Hubbard interactions have been reported to drive the insulating parent state of the superconductor from an integer quantum Hall (IQH) state to a chiral spin liquid (CSL). Our findings give credence to a recent proposal that proximity to the IQH-CSL transition serves to make chiral superconductivity energetically favorable on doping, and also correctly predicts the nature of the edge modes in the superconductor. On the CSL side, this suggests the superconductor can be thought of as arising from Laughlin's `anyon superconductivity' mechanism. Thus the Hubbard-Hofstadter model studied here offers a clean and experimentally accessible setup, potentially realizable in moiré heterostructures, for exploring the properties of anyonic matter at finite density and the interplay of topological order, quantum criticality and superconductivity.

Doping a spin-one Mott insulator: possible application to bilayer nickelate

Authors: Hanbit Oh, Hui Yang, Ya-Hui Zhang

arXiv ID: 2509.02673 | Date: 2025-09-02

Abstract: In this article, we review some recent theoretical developments on potential high-temperature superconductors and unconventional metallic states that can arise from doping a spin-one Mott insulator in the d8d^{8} valence. These studies are particularly relevant-though not limited-to the recently discovered bilayer nickelate superconductor La3_3Ni2_2O7_7. We focus on a ferromagnetic (FM) Kondo lattice model with mobile electrons in the dx2y2d_{x^2-y^2} orbital coupled to the localized spin moments in dz2d_{z^2} orbital through a large Hund's coupling JHJ_H. In the large JHJ_H limit, the model reduces to the type II t-J model with a mixture of spin-half singlon states and spin-one doublon states. We summarize DMRG results on the Luther-Emery liquid in one dimensional chain and two-leg ladder. Then we mainly focus on bilayer square lattice and show that a large inter-layer coupling JJ_\perp of dz2d_{z^2} orbital can induce strong inter-layer pairing of dx2y2d_{x^2-y^2} orbital. In the strong JJ_\perp limit, a kinetic-energy driven high TcT_c superconductivity is demonstrated in an ideal model with only a single hopping term. Furthermore, the model predicts a symmetric pseudogap metal-dubbed `second Fermi liquid"-in the underdoped regime, yielding a phase diagram analogous to that of hole-doped cuprates. The bilayer Kondo model therefore, presents a promising platform for both realizing higher-Tc superconductors and exploring non-Fermi liquid physics. We also comment on the possible limitations of the current models for the bilayer nickelate material and point out some future directions.

Semi-Dirac spin liquids and frustrated quantum magnetism on the trellis lattice

Authors: Sourin Chatterjee, Atanu Maity, Janik Potten, Tobias Müller, Andreas Feuerpfeil, Ronny Thomale, Karlo Penc, Harald O. Jeschke, Rhine Samajdar, Yasir Iqbal

arXiv ID: 2509.02663 | Date: 2025-09-02

Abstract: Geometrical frustration in quantum magnets provides a fertile setting for unconventional phases of matter, including quantum spin liquids (QSLs). The trellis lattice, with its complex site arrangements and edge-sharing triangular motifs, presents a promising platform for such physics. In this work, we undertake a comprehensive classification of all fully symmetric QSLs on the trellis lattice using the projective symmetry group approach within the Abrikosov fermion representation. We find 7 U(1) and 25 Z2\mathbb{Z}_{2} short-ranged Ansa¨tze\textit{Ansätze}, uncovering both gapped and Dirac QSLs as well as a novel semi-Dirac spin liquid, in which the spinon dispersion is linear along one momentum direction but quadratic along the orthogonal one. We demonstrate that such dispersions can occur only at high-symmetry points in the Brillouin zone with C2vC_{2v} little groups and analyze their characteristic correlation signatures. Moreover, by optimizing over all mean-field states, we map out a phase diagram -- featuring six distinct phases -- of the nearest-neighbor Heisenberg Hamiltonian on the trellis lattice. Going beyond mean field, we also assess equal-time and dynamical spin structure factors of these phases using density-matrix renormalization group and Keldysh pseudofermion functional renormalization group calculations. Finally, we identify four cuprate and vanadate compounds as promising experimental realizations and provide spectroscopic predictions, based on first-principles Hamiltonians, as a guide for future neutron-scattering studies on these materials.

Fermion Discretization Effects in the Two-Flavor Lattice Schwinger Model: A Study with Matrix Product States

Authors: Tim Schwägerl, Karl Jansen, Stefan Kühn

arXiv ID: 2509.02329 | Date: 2025-09-02

Abstract: We present a comprehensive tensor network study of staggered, Wilson, and twisted mass fermions in the Hamiltonian formulation, using the massive two-flavor Schwinger model as a benchmark. Particular emphasis is placed on twisted mass fermions, whose properties in this context have not been systematically explored before. We confirm the expected O(a) improvement in the free theory and observe that this improvement persists in the interacting case. By leveraging an electric-field-based method for mass renormalization, we reliably tune to maximal twist and establish the method's applicability in the two-flavor model. Once mass renormalization is included, the pion mass exhibits rapid convergence to the continuum limit. Finite-volume effects are addressed using two complementary approaches: dispersion relation fits and finite-volume scaling. Our results show excellent agreement with semiclassical predictions and reveal a milder volume dependence for twisted mass fermions compared to staggered and Wilson discretizations. In addition, we observe clear isospin-breaking effects, suggesting intriguing parallels with lattice QCD. These findings highlight the advantages of twisted mass fermions for Hamiltonian simulations and motivate their further exploration, particularly in view of future applications to higher-dimensional lattice gauge theories.

Probing Non-Fermi-Liquid Behaviour of Composite Fermi Liquid via Efficient Thermal Simulations

Authors: Bin-Bin Chen, Hongyu Lu, Zi Yang Meng

arXiv ID: 2509.02218 | Date: 2025-09-02

Abstract: The two-dimensional electron gas in a perpendicular magnetic field, i.e., the quantum Hall system, is remarkably rich. At half filling of the lowest Landau level, it has been predicted that ``composite fermions'' -- emergent quasiparticle of an electron with two magnetic flux quanta -- can experience zero net magnetic field and form a Fermi sea, dubbed composite Fermi liquid (CFL). However, the seemingly simple appearance of CFL is a strongly correlated quantum many-body state in disguise, and to solve it in a controlled manner is extremely difficult, to the level that the thermodynamic properties of CFL is still largely unknown. In this work, we perform state-of-the-art thermal tensor network simulations on the ν=1/2ν=1/2 Landau level systems, and observe low-temperature power-law behaviour of the specific heat, signaling the gapless nature of CFL. More importantly, the power is extracted to be closed to 2/32/3, clearly deviated from the ordinary linear-TT Fermi liquid behaviour, suggesting the coupling between the CFs and the dynamical emergent gauge field and therefore revealed the quantum many-body aspect of the CFL state. Relevance of our methodology to other quantum Hall settings and moiré systems is discussed.

Tensor renormalization group approach to entanglement entropy

Authors: Takahiro Hayazaki, Daisuke Kadoh, Shinji Takeda, Gota Tanaka

arXiv ID: 2509.02185 | Date: 2025-09-02

Abstract: We propose a method to compute the entanglement entropy (EE) using the tensor renormalization group (TRG) method. The reduced density matrix of a dd-dimensional quantum system is represented as a (d+1)(d+1)-dimensional tensor network. We develop an explicit algorithm for d=1d=1 that enables the calculation of EE for single-interval subsystems of arbitrary size. We test our method in two-dimensional tensor network of the Ising model. The central charge is obtained as c=0.49997(8)c=0.49997(8) for D=96D=96, which agrees with the theoretical prediction within an error, demonstrating the accuracy and reliability of our proposed method.

An Inexact Low-Rank Source Iteration for Steady-State Radiative Transfer Equation with Diffusion Synthetic Acceleration

Authors: Wei Guo, Zhichao Peng

arXiv ID: 2509.00805 | Date: 2025-08-31

Abstract: We propose an inexact low-rank source iteration with diffusion synthetic acceleration (SI-DSA) for solving the multidimensional steady-state radiative transfer equation (RTE) in the second-order formulation. The angular flux is represented in either a low-rank matrix or hierarchical Tucker tensor (HTT) format, enabling substantial reductions in computational resources. Each SI step is solved using a preconditioned low-rank conjugate gradient (CG) method with a diffusion preconditioner. To further improve efficiency, we introduce an adaptive inexact strategy that dynamically relaxes the inner CG tolerance during early SI iterations. The method exploits the tensor-product structure of the discretized operators to perform all matrix-vector operations in low-rank form. Numerical experiments on 2D2V benchmark problems, including diffusion-dominated, transport-dominated, and multiscale problems, demonstrate that the proposed approach achieves errors on the order of 10410^{-4} to 10510^{-5} relative to full-rank reference solutions, while reducing the degrees of freedom by up to two orders of magnitude. In the diffusion-dominated case, the low-rank solver achieves speedups exceeding 90×90\times over its full-rank counterpart and remains competitive in solving challenging transport-dominated and multiscale problems while providing substantial storage savings. To our knowledge, this work provides the first low-rank SI-DSA framework for multidimensional steady-state RTE.

Electronic frictional effects near metal surfaces with strong correlations

Authors: Yunhao Liu, Wenjie Dou

arXiv ID: 2509.00682 | Date: 2025-08-31

Abstract: The electronic friction-Langevin dynamics (EF-LD) offers a simplified framework for describing nonadiabatic effects at metal surfaces, particularly in electrochemical and molecular electronic applications. We investigate the electronic friction behavior for the Hubbard-Holstein model using density matrix renormalization group (DMRG) theory. We show that electron-electron interactions lead to the formation of two energy levels in the impurity, resulting in two peaks in the electronic friction at the resonances of electron attachment or detachment with the metal's Fermi level. We further benchmark our results against mean field theory (MFT) and exact diagonalization (ED). The results calculated by ED and DMRG show strong agreement at high temperatures, suggesting the results from DMRG are reliable; however, at low temperatures, ED exhibits significant deviations relative to DMRG due to the finite-size limitations inherent in ED calculations. MFT completely fails to recover Fermi resonance in electronic friction. Moreover, we investigate the dynamics of the electronic friction using EF-LD. Simulations reveal differences between the electronic population and kinetic energy dynamics predicted by MFT and DMRG approaches, suggesting that MFT approach is unreliable for nonadiabatic dynamics of strongly correlated systems.

A Further Comparison of MPS and TTNS for Nonadiabatic Dynamics of Exciton Dissociation

Authors: Weitang Li, Jiajun Ren, Jun Yan

arXiv ID: 2509.00456 | Date: 2025-08-30

Abstract: Tensor networks, such as matrix product states (MPS) and tree tensor network states (TTNS), are powerful ansätze for simulating quantum dynamics. While both ansätze are theoretically exact in the limit of large bond dimensions, [J. Chem. Theory Comput. 2024, 20, 8767-8781] reported a non-negligible discrepancy in its calculations for exciton dissociation. To resolve this inconsistency, we conduct a systematic comparison using Renormalizer, a unified software framework for MPS and TTNS. By revisiting the benchmark P3HT:PCBM heterojunction model, we show that the observed discrepancies arise primarily from insufficient bond dimensions. By increasing bond dimensions, we reduce the relative difference in occupancy for weakly populated electronic states from up to 60% towards the end of the simulation to less than 10% and the absolute difference from 0.05 to 0.005. We also discuss the impact of tensor network structures on accuracy and efficiency, with the difference further reduced by an optimized TTNS structure. Our results confirm that both methods converge to numerically exact solutions when bond dimensions are adequately scaled. This work not only validates the reliability of both methods but also provides high-accuracy benchmark data for future developments in quantum dynamics simulations.

Polynomial complexity of open quantum system problems

Authors: Chong Chen, Ren-Bao Liu

arXiv ID: 2509.00424 | Date: 2025-08-30

Abstract: Open quantum systems (OQS's) are ubiquitous in non-equilibrium quantum dynamics and in quantum science and technology. Solving the dynamics of an OQS in a quantum many-body bath has been considered a computationally hard problem because of the dimensionality curse. Here, considering that full knowledge of the bath dynamics is unnecessary for describing the reduced dynamics of an OQS, we prove a polynomial complexity theorem, that is, the number of independent equations required to fully describe the dynamics of an OQS increases at most linearly with the evolution time and polynomially with the bath size. Therefore, efficient computational algorithms exist for solving the dynamics of a small-sized OQS (such as a qubit or an atom). We further prove that, when the dynamics of an OQS and the bath is represented by a tensor network, a tensor contraction procedure can be specified such that the bond dimension (i.e., the range of tensor indices contracted in each step) increases only linearly (rather than exponentially) with the evolution time, providing explicitly efficient algorithms for a wide range of OQS's. We demonstrate the theorems and the tensor-network algorithm by solving two widely encountered OQS problems, namely, a spin in a Gaussian bath (the spin-boson model) and a central spin coupled to many environmental spins (the Gaudin model). This work provides approaches to understanding dynamics of OQS's, learning the environments via quantum sensors, and optimizing quantum information processing in noisy environments.

Remote spin control in Haldane spin chains

Authors: Y. del Castillo, A. Ferrón, J. Fernández-Rossier

arXiv ID: 2508.21544 | Date: 2025-08-29

Abstract: We consider the remote manipulation of the quantum state of the edge fractional spins of Haldane spin chains using a weak local perturbation on the other edge. We derive an effective four-level model that correctly captures the response of the local magnetization to local perturbations and we use it to show that applying a small local field on one edge of the chain induces a strong variation of the magnetization on the opposite edge. Using a Landau-Zener protocol, we show how local control of the field on one edge of the chain, implemented for instance with a spin-polarized scanning tunnel microscope tip, can adiabatically switch the magnetization direction on the other side of the chain.

Determination of ground states of one-dimensional quantum systems using the cluster iTEBD method

Authors: Tao Yang, Rui Wang, Z. Y. Xie, Baigeng Wang

arXiv ID: 2508.21405 | Date: 2025-08-29

Abstract: Within the framework of imaginary-time evolution for matrix product states, we introduce a cluster version of the infinite time-evolving block decimation algorithm for simulating quantum many-body systems, addressing the computational accuracy challenges in strongly correlated physics. By redefining the wave-function ansatz to incorporate multiple physical degrees of freedom, we enhance the representation of entanglement, thereby improving the accuracy of the ground states. Utilizing the Trotter-Suzuki decomposition and optimized truncation schemes, our method maintains roughly the same computational complexity while capturing more quantum correlations. We apply this approach to three nontrivial cases: the gapless spin-1/2 Heisenberg chain, the spin-1 anisotropic XXZD chain with a higher-order Gaussian-type phase transition, and a spin-1/2 twisted triangular prism hosting a magnetic plateau phase. Improved accuracy in physical quantities, such as magnetization, ground-state energy, and entanglement entropy, has been demonstrated. This method provides a scalable framework for studying complex quantum systems with high precision, making it suitable for situations where a pure increase in bond dimension alone cannot guarantee satisfactory results.

Reinforcement Learning for Optimizing Large Qubit Array based Quantum Sensor Circuits

Authors: Laxmisha Ashok Attisara, Sathish Kumar

arXiv ID: 2508.21253 | Date: 2025-08-28

Abstract: As the number of qubits in a sensor increases, the complexity of designing and controlling the quantum circuits grows exponentially. Manually optimizing these circuits becomes infeasible. Optimizing entanglement distribution in large-scale quantum circuits is critical for enhancing the sensitivity and efficiency of quantum sensors [5], [6]. This paper presents an engineering integration of reinforcement learning with tensor-network-based simulation (MPS) for scalable circuit optimization for optimizing quantum sensor circuits with up to 60 qubits. To enable efficient simulation and scalability, we adopt tensor network methods, specifically the Matrix Product State (MPS) representation, instead of traditional state vector or density matrix approaches. Our reinforcement learning agent learns to restructure circuits to maximize Quantum Fisher Information (QFI) and entanglement entropy while reducing gate counts and circuit depth. Experimental results show consistent improvements, with QFI values approaching 1, entanglement entropy in the 0.8-1.0 range, and up to 90% reduction in depth and gate count. These results highlight the potential of combining quantum machine learning and tensor networks to optimize complex quantum circuits under realistic constraints.

Nonperturbative Semiclassical Spin Dynamics for Ordered Quantum Magnets

Authors: Hao Zhang, Tianyue Huang, Allen O. Scheie, Mengze Zhu, Tao Xie, N. Murai, S. Ohira-Kawamura, Andrey Zheludev, Andreas M. Läuchli, Cristian D. Batista

arXiv ID: 2508.21142 | Date: 2025-08-28

Abstract: In ordered quantum magnets where interactions between elementary excitations dominate over their kinetic energy, perturbative approaches often fail, making non-perturbative methods essential to capture spectral features such as bound states and the redistribution of weight within excitation continua. Although an increasing number of experiments report anomalous spin excitation continua in such systems, their microscopic interpretation remains an open challenge. Here, we investigate the spin dynamics of the triangular-lattice antiferromagnet in its 1/3-plateau phase using two complementary non-perturbative approaches: exact diagonalization in a truncated Hilbert space for a gas of elementary excitations (THED) and matrix product state (MPS) simulations. Alongside cross-validation between these methods, we benchmark our results against inelastic neutron scattering (INS) data. The THED analysis confirms the presence of two-magnon bound states and identifies the anomalous scattering continuum observed in both MPS and INS as a two-magnon resonance, arising from hybridization between the bound state and the two-magnon continuum. Furthermore, THED reveals bound states overlapping with the continuum, enriching the interpretation of continuum anomalies. More broadly, THED provides a robust framework for investigating anomalous spin excitation continua and bound-state effects in other materials with gapped spectra. Its combination of accuracy and computational efficiency makes it a powerful tool for extracting reliable microscopic models in semiclassical regimes.

Quantum algorithms for equational reasoning

Authors: Davide Rattacaso, Daniel Jaschke, Marco Ballarin, Ilaria Siloi, Simone Montangero

arXiv ID: 2508.21122 | Date: 2025-08-28

Abstract: We introduce quantum normal form reduction, a quantum computational framework for analyzing abstract symbolic expressions - such as strings, algebraic formulas, or quantum circuits - that are equivalent under a given set of transformation rules. These rules form a term rewriting system, a formal method for deriving equivalences by repeatedly applying substitutions. We construct an efficiently implementable quantum Hamiltonian whose ground state encodes the entire class of equivalent expressions - potentially exponentially many - in a quantum superposition. By preparing and manipulating these ground states, we address fundamental problems in equational reasoning, including the word problem, i.e., determining whether two expressions are equivalent, counting the number of equivalent expressions, and identifying structural properties of equivalence classes. We demonstrate a quantum-inspired version of the algorithm using tensor network simulations by solving instances involving up to 102810^{28} equivalent expressions, well beyond the reach of standard classical graph exploration techniques. This framework opens the path for quantum symbolic computation in areas ranging from quantum and logical circuit design to data compression, computational group theory, linguistics, polymers and biomolecular modeling, enabling the investigation of problems previously out of reach.

Evolution of quasiparticle edge states with Hubbard interaction in Rice-Mele chain

Authors: Jyoti Bisht, Brijesh Kumar

arXiv ID: 2508.21008 | Date: 2025-08-28

Abstract: We study the behaviour of edge states in Rice-Mele model with Hubbard interaction, U , at half-filling using density matrix renormalization group, exact diagonalization and effective charge dynamics in Kumar representation. For a fixed dimerization, δδ, and staggered potential, V , we find by increasing U the quasiparticle edge states in the charge gap to come down in energy from V in the absence of Hubbard interaction to zero energy for U \approx 2V . This presents an uncommon case where repulsion leads to zero-energy edge states. Upon increasing U further, the edge state energy starts increasing again until they are lost in the bulk. However, upon increasing U even further, these edge states reappear in the high energy gap. So, with Hubbard interaction, the edge states in Rice-Mele chain transmigrate from the physical charge gap to a high energy gap.

Classical fractional time series from quantum XXZ spin chains

Authors: Zoltán Udvarnoki, Gábor Fáth, Miklós Werner, Örs Legeza

arXiv ID: 2508.20974 | Date: 2025-08-28

Abstract: Entangled quantum mechanical states in one dimension can be used to represent and simulate classical stochastic processes with nontrivial statistical properties. Long-range quantum correlations translate into fractional processes with their asymptotic Hurst exponents characterizing roughness and persistence. We explore this analogy in the case of the spin-1/2 XXZ chain and investigate properties of four different classical two-state processes that this quantum system can generate. These processes show fractional characteristics with varying Hurst exponents. We argue that the continuous quantum symmetries such as U(1) or SU(2) of the XXZ chain give rise to H=0H=0 with logarithmic scaling. Processes generated without these symmetries can produce H0.5H \geq0.5 but likely not H<0.5H < 0.5 unless the dominant term responsible for H=0.5H=0.5 gets canceled. This does not seem to happen for the XXZ model. We use standard quantum methods, including MERA and TEBD, to numerically substantiate our findings.

Optimization on the Extended Tensor-Train Manifold with Shared Factors

Authors: Alexander Molozhavenko, Maxim Rakhuba

arXiv ID: 2508.20928 | Date: 2025-08-28

Abstract: This paper studies tensors that admit decomposition in the Extended Tensor Train (ETT) format, with a key focus on the case where some decomposition factors are constrained to be equal. This factor sharing introduces additional challenges, as it breaks the multilinear structure of the decomposition. Nevertheless, we show that Riemannian optimization methods can naturally handle such constraints and prove that the underlying manifold is indeed smooth. We develop efficient algorithms for key Riemannian optimization components, including a retraction operation based on quasi-optimal approximation in the new format, as well as tangent space projection using automatic differentiation. Finally, we demonstrate the practical effectiveness of our approach through tensor approximation tasks and multidimensional eigenvalue problem.

Equally entangled multiqubit states

Authors: Francisco Albarrán-Arriagada, Guillermo Romero, Juan Carlos Retamal

arXiv ID: 2508.20770 | Date: 2025-08-28

Abstract: We present a protocol for generating multiqubit quantum states with translationally invariant pairwise entanglement. Our approach is tailored for digital quantum computers with restricted qubit connectivity, a common limitation in state-of-the-art hardware platforms. We examine two configurations: star connectivity, which enables rotationally invariant entanglement, and linear connectivity, which achieves translationally invariant entanglement. For the linear configuration, we use a variant of the time-dependent density matrix renormalization group (tDMRG) algorithm to demonstrate that our protocol is independent of the qubits' number. A slight modification of the protocol reveals the presence of quantum states that exhibit periodicity of entanglement among nearest-neighbor qubits. The configurations and protocols of this work are well-suited for near-term quantum devices, offering a feasible route for the experimental realization of symmetric entangled states.

Classical Simulations of Low Magic Quantum Dynamics

Authors: Kemal Aziz, Haining Pan, Michael J. Gullans, J. H. Pixley

arXiv ID: 2508.20252 | Date: 2025-08-27

Abstract: We develop classical simulation algorithms for adaptive quantum circuits that produce states with low levels of ``magic'' (i.e., non-stabilizerness). These algorithms are particularly well-suited to circuits with high rates of Pauli measurements, such as those encountered in quantum error correction and monitored quantum circuits. The measurements serve to limit the buildup of magic induced by non-Clifford operations arising from generic noise processes or unitary gates, respectively. Our algorithms also allow a systematic truncation procedure to achieve approximate simulation. To benchmark our approach, we study the dynamics of all-to-all monitored quantum circuits with a sub-extensive rate of T-gates per unit of circuit depth, where we can simulate previously inaccessible system sizes and depths. We characterize measurement-induced phase transitions in the output wavefunction, including in the entanglement, purification, and magic. We outline the utility of our algorithms to simulate dynamics with low magic and high entanglement, complementary to the leading matrix-product state approaches.

Near-optimal decomposition of unitary matrices using phase masks and the discrete Fourier transform

Authors: Vincent Girouard, Nicolás Quesada

arXiv ID: 2508.20010 | Date: 2025-08-27

Abstract: Universal multiport interferometers (UMIs) have emerged as a key tool for performing arbitrary linear transformations on optical modes, enabling precise control over the state of light in essential applications of classical and quantum information processing such as neural networks and boson sampling. While UMI architectures based on Mach-Zehnder interferometer networks are well established, alternative approaches that involve interleaving fixed multichannel mixing layers and phase masks have recently gained interest due to their high robustness to losses and fabrication errors. However, these approaches currently lack optimal analytical methods to compute design parameters with low optical depth. In this work, we introduce a constructive decomposition of unitary matrices using a sequence of 2N+52N+5 phase masks interleaved with 2N+42N+4 discrete Fourier transform matrices. This decomposition can be leveraged to design universal interferometers based on phase masks and multimode interference couplers, implementing a discrete Fourier transform, offering an analytical alternative to conventional numerical optimization-based designs and reducing by a factor of 3 the previous best known analytical methods.

Direct probing of the simulation complexity of open quantum many-body dynamics

Authors: Lucia Vilchez-Estevez, Alexander Yosifov, Jinzhao Sun

arXiv ID: 2508.19959 | Date: 2025-08-27

Abstract: Simulating open quantum systems is key to understanding non-equilibrium processes, as persistent influence from the environment induces dissipation and can give rise to steady-state phase transitions. A common strategy is to embed the system-environment into a larger unitary framework, but this obscures the intrinsic complexity of the reduced system dynamics. Here, we investigate the computational complexity of simulating open quantum systems, focusing on two physically relevant parameters -- correlation length and mixing time -- and explore whether it can be comparable (or even lower) to that of simulating their closed counterparts. In particular, we study the role of dissipation in simulating open-system dynamics using both quantum and classical methods, where the classical complexity is characterised by the bond dimension and operator entanglement entropy. Our results show that dissipation affects correlation length and mixing time in distinct ways at intermediate and long timescales. Moreover, we observe numerically that in classical tensor network simulations, classical complexity does not decrease with stronger dissipation, revealing a separation between quantum and classical resource scaling.

Numerical Optimization for Tensor Disentanglement

Authors: Julia Wei, Alec Dektor, Chungen Shen, Zaiwen Wen, Chao Yang

arXiv ID: 2508.19409 | Date: 2025-08-26

Abstract: Tensor networks provide compact and scalable representations of high-dimensional data, enabling efficient computation in fields such as quantum physics, numerical partial differential equations (PDEs), and machine learning. This paper focuses on tensor disentangling, the task of identifying transformations that reduce bond dimensions by exploiting gauge freedom in the network. We formulate this task as an optimization problem over orthogonal matrices acting on a single tensor's indices, aiming to minimize the rank of its matricized form. We present Riemannian optimization methods and a joint optimization framework that alternates between optimizing the orthogonal transformation for a fixed low-rank approximation and optimizing the low-rank approximation for a fixed orthogonal transformation, offering a competitive alternative when the target rank is known. To seek the often unknown optimal rank, we introduce a binary search strategy integrated with the disentangling procedure. Numerical experiments on random tensors and tensors in an approximate isometric tensor network state are performed to compare different optimization methods and explore the possibility of combining different methods in a hybrid approach.

Entanglement Hamiltonian after a local quench

Authors: Riccarda Bonsignori, Viktor Eisler

arXiv ID: 2508.19406 | Date: 2025-08-26

Abstract: We investigate the dynamics of the entanglement Hamiltonian in a system of one-dimensional free fermions, following a local joining quench of two initially disconnected half-chains in their ground states. Applying techniques of conformal field theory, we obtain a local expression where the left- and right-moving components of the energy density are associated with different weight functions. The results are then compared to numerical calculations for the hopping chain, which requires to consider a proper continuum limit of the lattice entanglement Hamiltonian, obtaining a good agreement with the field-theory prediction.

Thermodynamics in a split Hilbert space: Quantum impurity at the edge of the Heisenberg chain

Authors: Abay Zhakenov, Pradip Kattel, Natan Andrei

arXiv ID: 2508.19334 | Date: 2025-08-26

Abstract: We study the isotropic spin-12\frac{1}{2} Heisenberg chain with a single edge-coupled impurity of arbitrary exchange strength JJ. The model exhibits four impurity phases. For antiferromagnetic couplings (J>0J>0): a \textit{Kondo phase} at weak JJ, where the impurity is screened by many-body excitations and the impurity entropy decreases monotonically from ln2\ln 2 at TT \to \infty to 00 at T0T\to 0; and an \textit{antiferromagnetic bound-mode (ABM) phase} at strong JJ, where the impurity screened by an exponentially localized bound mode drives Simp(T)S_{\mathrm{imp}}(T) nonmonotonically, with undershoots below zero at intermediate temperatures, while tending to ln2\ln 2 as TT \to \infty and to 00 as T0T \to 0. For ferromagnetic couplings (J<0J<0): a local-moment (LM) phase at weak J|J|, where the impurity remains unscreened with Simpln2S_{\mathrm{imp}}\to \ln 2 as T0T \to 0 but exhibits shallow undershoots at intermediate scales; and a \textit{ferromagnetic bound-mode (FBM) phase} at strong J|J|, where Simp=ln2S_{\mathrm{imp}}=\ln 2 in both UV and IR limits, yet develops an intermediate-temperature undershoot. We provide an analytic understanding of this behavior, showing that the undershoots originate from the fractionalization of the Hilbert space into several towers of states: for antiferromagnetic couplings this occurs only at strong JJ, driven by boundary-localized bound modes, while for ferromagnetic couplings undershoots occur for all J<0J<0, becoming deeper with increasing J|J| and vanishing as J0J\to 0^{-}. These bound modes screen the impurity. Incorporating the bound modes and edge states provides a complete analytic understanding of this phenomenon and yields closed expressions for the impurity contribution to free energy and entropy that are valid across all phases. These are checked and found to be in excellent agreement with tensor network and exact diagonalization results.

Tunneling spectroscopy of the spinon-Kondo effect in one-dimensional Mott insulators

Authors: Rodrigo G. Pereira, Bruno F. Marquez, Karen Hallberg, Tim Bauer, Reinhold Egger

arXiv ID: 2508.19084 | Date: 2025-08-26

Abstract: We study the tunneling density of states (TDOS) in one-dimensional Mott insulators at energies below the charge gap. By employing nonlinear Luttinger liquid theory and density-matrix renormalization group (DMRG) simulations, we predict that in the presence of a magnetic impurity at the boundary, characteristic Fermi-edge singularity features can appear at subgap energies in the TDOS near the boundary. In contrast to the Kondo effect in a metal, these resonances are strongly asymmetric and of power-law form. The power-law exponent is universal and determined by the spinon-Kondo effect.

Scalable Effective Models for Superconducting Nanostructures: Applications to Double, Triple, and Quadruple Quantum Dots

Authors: Daniel Bobok, Lukáš Frk, Vladislav Pokorný, Martin Žonda

arXiv ID: 2508.18465 | Date: 2025-08-25

Abstract: We introduce a versatile and scalable framework for constructing effective models of superconducting (SC) nanostructures described by the generalized SC Anderson impurity model with multiple quantum dots and leads. Our Chain Expansion (ChE) method maps each SC lead onto a finite tight-binding chain with parameters obtained from \emph{Padé} approximants of the tunneling self-energy. We provide an explicit algorithm for the general case as well as simple analytical expressions for the chain parameters in the wide-band and infinite-chain limits. This mapping preserves low-energy physics while enabling efficient simulations: short chains are tractable using exact diagonalization, and longer ones are handled with density matrix renormalization group methods. The approach remains reliable and computationally efficient across diverse geometries, both in and out of equilibrium. We use ChE to map the ground-state phase diagrams of double, triple, and quadruple quantum dots coupled to a single SC lead. While half-filled symmetric systems show similar overall diagrams, the particular phases differ substantially with the dot number. Here, large parameter regions are entirely missed by the widely used zero-bandwidth approximation but are captured by ChE. Away from half-filling, additional dots markedly increase diagram complexity, producing a rich variety of stable phases. These results demonstrate ChE as a fast, accurate, and systematically improvable tool for exploring complex SC nanostructures.

Low-Rank Tensor Decompositions for the Theory of Neural Networks

Authors: Ricardo Borsoi, Konstantin Usevich, Marianne Clausel

arXiv ID: 2508.18408 | Date: 2025-08-25

Abstract: The groundbreaking performance of deep neural networks (NNs) promoted a surge of interest in providing a mathematical basis to deep learning theory. Low-rank tensor decompositions are specially befitting for this task due to their close connection to NNs and their rich theoretical results. Different tensor decompositions have strong uniqueness guarantees, which allow for a direct interpretation of their factors, and polynomial time algorithms have been proposed to compute them. Through the connections between tensors and NNs, such results supported many important advances in the theory of NNs. In this review, we show how low-rank tensor methods--which have been a core tool in the signal processing and machine learning communities--play a fundamental role in theoretically explaining different aspects of the performance of deep NNs, including their expressivity, algorithmic learnability and computational hardness, generalization, and identifiability. Our goal is to give an accessible overview of existing approaches (developed by different communities, ranging from computer science to mathematics) in a coherent and unified way, and to open a broader perspective on the use of low-rank tensor decompositions for the theory of deep NNs.

The holographic dual of the GHZ state

Authors: Libo Jiang, Yan Liu

arXiv ID: 2508.17898 | Date: 2025-08-25

Abstract: Current holographic research mostly focuses on a subset of quantum systems with a classical gravity dual. Although the precise boundary of this subset remains unknown, certain constraints are recognized; for instance, holographic entropies obey inequalities that are violated by general quantum states such as the GHZ states. This paper, however, presents a gravity dual for GHZ states -- a non-ordinary geometry termed the booklet wormhole. We demonstrate an exact match for all entropy properties with the GHZ state, as well as the identity of the Euclidean partition functions for both systems. The booklet wormhole circumvents the conventional holographic entropy inequalities because different topologies are inevitably included in the gravitational path integral, even in the large-NN limit. This provides the first explicit holographic duality with a non-perturbative quantum effect. Remarkably, the construction is simple and maximally entangled, making it ideal for gedanken experiments.

Succession of Ising criticality and its threshold in critical quantum Ising model subject to symmetric decoherence

Authors: Yoshihito Kuno, Takahiro Orito, Ikuo Ichinose

arXiv ID: 2508.17871 | Date: 2025-08-25

Abstract: We investigate a mixed state quantum criticality in the Ising model under X+ZZX+ZZ decoherence. In the doubled Hilbert space formalism, the decohered state resides on the self-dual critical line of the quantum Ashkin-Teller (qAT) model, as a result of the specific choice of the decoherence channel. On the other hand, since the mixed state under X+ZZX+ZZ decoherence satisfies the Kramers-Wannier self-duality in a weak sense, the Ising criticality of the pure state can be partially preserved in the mixed system. By making use of the combination of the doubled Hilbert space formalism and matrix product states, we carry out extensive numerical study to elucidate the mixed state criticality. We find that under decoherence up to moderate strength, the mixed states on the critical line have properties of the Ising CFT, where c=1/2c=1/2, η=0.25η=0.25 and, ν=1ν=1. These values of the central charge and critical exponents contrast with the ones in the c=1c=1 orbifold boson CFT describing the critical state of the qAT model. In addition, we also observe the threshold of the mixed Ising CFT. The strong decoherence washes out the remnant Ising criticality and induces strong-to-weak spontaneous symmetry breaking.

Zeeman Ladders in Frustrated XYZ Spin Chains

Authors: Catalin-Mihai Halati, Viola Romerio, Paul Steffens, J. Ross Stewart, Andrey Zheludev, Thierry Giamarchi

arXiv ID: 2508.17834 | Date: 2025-08-25

Abstract: We investigate the nature of the excitations captured by the dynamical response of XYZ triangular spin-1/2 ladders. We complement experimental inelastic neutron scattering results on the compound Cs2CoBr4\text{Cs}_\text{2}\text{CoBr}_\text{4} with numerically exact simulations based on time-dependent matrix product state methods. Our results show that bound states of spinon excitations can arise in XYZ beyond the requirement of strong Ising anisotropies. We analyze the role of the frustrated triangular couplings on the excitations giving rise to the spin dynamical structure factor and show how the features of the bound states manifest themselves in the different polarization channels.

Spectral Functions of an Extended Antiferromagnetic S=1/2S=1/2 Heisenberg Model on the Triangular Lattice

Authors: Markus Drescher, Laurens Vanderstraeten, Roderich Moessner, Frank Pollmann

arXiv ID: 2508.17292 | Date: 2025-08-24

Abstract: We study an extended spin-1/21/2 antiferromagnetic Heisenberg model on the triangular lattice, which includes both nearest- and next-nearest-neighbor interactions, as well as a scalar chiral term. This model exhibits a rich phase diagram featuring several competing phases: different quantum spin liquids and various magnetically ordered states, including coplanar 120120^\circ order, stripe order, and non-coplanar tetrahedral order. We employ large-scale matrix product state simulations optimized for GPUs to obtain high-resolution dynamical responses. Our calculations reveal the spectral features across both ordered and liquid regimes of the phase diagram, which we analyze in comparison with analytical predictions and field-theoretical approaches. We identify unique signatures of the ordered phases in the form of gapless Goldstone modes at the ordering wave vectors. Our results in the J1J2J_1-J_2 quantum spin-liquid regime are indicative of a U(1)U(1) Dirac spin liquid. In the chiral spin-liquid phase, we find signatures of spinons as the fractional excitations of the underlying theory, manifested as the onset of a two-spinon continuum that agrees with predictions from the Kalmeyer-Laughlin ansatz for the ground-state wave function, and collective modes that can be viewed as spinon bound states. We discuss finite-size effects, their consistency with the presumptions from field-theory, and review the dynamical structure factor with regard to experimentally relevant features such as the occurrence of highly dispersive signals and the global distribution of spectral weight.

The holographic entanglement pattern of BTZ planar black hole from a thread perspective

Authors: Yi-Yu Lin, Dong-Yu Fang, Jie-Chen Jin, Chen-Ye Li

arXiv ID: 2508.16977 | Date: 2025-08-23

Abstract: In this paper, we study the holographic quantum entanglement structure in the finite-temperature CFT state/planar BTZ black hole correspondence from the perspective of entanglement threads. Unlike previous studies based on bit threads, these entanglement threads provide a more detailed characterization of the contribution sources to the von Neumann entropy of boundary subregions, in particular by quantitatively deriving the flux function of entanglement threads that traverse the wormhole horizon and connect the two asymptotic boundaries. Since entanglement threads are naturally and closely related to tensor network states, the results are argued to imply the existence of the perfect-type entanglement formed jointly by the entanglement threads crossing the wormhole and the internal threads in the single-sided boundary. We also discuss the close connections of this work with concepts such as bit threads and partial entanglement entropy.

Unitary network: Tensor network unitaries with local unitarity

Authors: Wenqing Xie, Seishiro Ono, Hoi Chun Po

arXiv ID: 2508.16890 | Date: 2025-08-23

Abstract: We introduce unitary network, an oriented architecture for tensor network unitaries. Compared to existing architectures, in a unitary network each local tensor is required to be a unitary matrix upon suitable reshaping. Global unitarity is ensured when the network obeys a suitable ordering property. Unitary operators represented by unitary networks need not preserve locality. In particular, we show that the class of unitary networks encompasses global unitaries which preserve locality up to exponentially suppressed tails, as in those that naturally arise from the finite-time evolution of local Hamiltonians. Non-invertible symmetries, as exemplified by the non-local Kramers-Wannier duality in one dimension, can also be represented using unitary networks. We also show that information flow in a unitary network can be characterized by a flow index, which matches the known index for quantum cellular automata as a special case.

Hunting for superconductivity in doped triangular lattice Kitaev magnets

Authors: Andrew Hardy, Ryan Levy, Arun Paramekanti

arXiv ID: 2508.16720 | Date: 2025-08-22

Abstract: Motivated by exploring correlated metals with frustrating bond-dependent exchange interactions, we study hole and electron doped Kitaev Mott insulators on the triangular lattice. Using homogeneous parton mean field theory, we find that the stripe antiferromagnetic (AFM) order for Kitaev coupling K>0K>0 and the ferromagnetic (FM) order for K<0K<0, both vanish at sufficiently large doping, beyond which we find regimes with chiral d±idd\pm i d singlet pairing and p±ipp\pm ip triplet pairing respectively. Our tensor network computations however reveal that the superconducting correlations are strongly suppressed; while FM order stubbornly persists for the doped K<0K<0 model, the doped K>0K>0 model features emergent spin-charge modulated stripe orders. At higher hole doping for K>0K > 0, where AFM order is more strongly suppressed than for the electron doped case, incorporating a sufficiently strong nearest-neighbor attraction yields evidence for singlet dd-wave superconductivity with Luttinger parameter Ksc<1K_{\rm sc} < 1. Our work sets the stage for a broader exploration of doping effects in triangular lattice magnets such as NaRuO2_2 which feature bond-dependent exchange interactions.

Emergent statistical mechanics in holographic random tensor networks

Authors: Shozab Qasim, Jens Eisert, Alexander Jahn

arXiv ID: 2508.16570 | Date: 2025-08-22

Abstract: Recent years have enjoyed substantial progress in capturing properties of complex quantum systems by means of random tensor networks (RTNs), which form ensembles of quantum states that depend only on the tensor network geometry and bond dimensions. Of particular interest are RTNs on hyperbolic geometries, with local tensors typically chosen from the unitary Haar measure, that model critical boundary states of holographic bulk-boundary dualities. In this work, we elevate static pictures of ensemble averages to a dynamical one, to show that RTN states exhibit equilibration of time-averaged operator expectation values under a highly generic class of Hamiltonians with non-degenerate spectra. We prove that RTN states generally equilibrate at large bond dimension and also in the scaling limit for three classes of geometries: Those of matrix product states, regular hyperbolic tilings, and single "black hole" tensors. Furthermore, we prove a hierarchy of equilibration between finite-dimensional instances of these classes for bulk and boundary states with small entanglement. This suggests an equivalent hierarchy between corresponding many-body phases, and reproduces a holographic degree-of-freedom counting for the effective dimension of each system. These results demonstrate that RTN techniques can probe aspects of late-time dynamics of quantum many-body phases and suggest a new approach to describing aspects of holographic dualities using techniques from statistical mechanics.

Infinite matrix product states for (1+1)(1+1)-dimensional gauge theories

Authors: Ross Dempsey, Anna-Maria E. Glück, Silviu S. Pufu, Benjamin T. Søgaard

arXiv ID: 2508.16363 | Date: 2025-08-22

Abstract: We present a matrix product operator construction that allows us to represent the lattice Hamiltonians of (abelian or non-abelian) gauge theories in a local and manifestly translation-invariant form. In particular, we use symmetric matrix product states and introduce link-enhanced matrix product operators (LEMPOs) that can act on both the physical and virtual spaces of the matrix product states. This construction allows us to study Hamiltonian lattice gauge theories on infinite lattices. As examples, we show how to implement this method to study the massless and massive one-flavor Schwinger model and adjoint QCD2_2.

Statistics-encoded tensor network approach in disordered quantum many-body spin chains

Authors: Hao Zhu, Ding-Zu Wang, Shi-Ju Ran, Guo-Feng Zhang

arXiv ID: 2508.16286 | Date: 2025-08-22

Abstract: Simulating the dynamics of quantum many-body systems with disorder is a fundamental challenge. In this work, we propose a general approach -- the statistics-encoded tensor network (SeTN) -- to study such systems. By encoding disorder into an auxiliary layer and averaging separately, SeTN restores translational invariance, enabling a well-defined transfer matrix formulation. We derive a universal criterion, nα2t2n \gg α^2 t^2, linking discretization nn, disorder strength αα, and evolution duration tt. This sets the resolution required for faithful disorder averaging and shows that encoding is most efficient in the weak-disorder, typically chaotic regime. Applied to the disordered transverse-field Ising model, SeTN shows that the spectral form factor is governed by the leading transfer-matrix eigenvalue, in contrast to the kicked Ising model. SeTN thus provides a novel framework for probing the disorder-driven dynamical phenomena in many-body quantum systems.

Evaluating classical simulations with a quantum processor

Authors: Alberto Nocera, Jack Raymond, William Bernoudy, Mohammad H. Amin, Andrew D. King

arXiv ID: 2508.15759 | Date: 2025-08-21

Abstract: As simulations of quantum systems cross the limits of classical computability, both quantum and classical approaches become hard to verify. Scaling predictions are therefore based on local structure and asymptotic assumptions, typically with classical methods being used to evaluate quantum simulators where possible. Here, in contrast, we use a quantum annealing processor to produce a ground truth for evaluating classical tensor-network methods whose scaling has not yet been firmly established. Our observations run contrary to previous scaling predictions, demonstrating the need for caution when extrapolating the accuracy of classical simulations of quantum dynamics. Our results demonstrate that the virtuous cycle of competition between classical and quantum simulations can lend insight in both directions.

Assessing the Reliability of Truncated Coupled Cluster Wavefunction: Estimating the Distance from the Exact Solution

Authors: Ádám Ganyecz, Zsolt Benedek, Klára Petrov, Gergely Barcza, András Olasz, Miklós A. Werner, Örs Legeza

arXiv ID: 2508.15681 | Date: 2025-08-21

Abstract: A new approach is proposed to assess the reliability of the truncated wavefunction methods by estimating the deviation from the full configuration interaction (FCI) wavefunction. While typical multireference diagnostics compare some derived property of the solution with the ideal picture of a single determinant, we try to answer a more practical question, how far is the solution from the exact one. Using the density matrix renormalization group (DMRG) method to provide an approximate FCI solution for the self-consistently determined relevant active space, we compare the low-level CI expansions and one-body reduced density matrixes to determine the distance of the two solutions (d~Φ\tilde{d}_Φ, d~γ\tilde{d}_γ). We demonstrate the applicability of the approach for the CCSD method by benchmarking on the W4-17 dataset, as well as on transition metal-containing species. We also show that the presented moderate-cost, purely wavefunction-based metric is truly unique in the sense that it does not correlate with any popular multireference measures. We also explored the usage of CCSD natural orbitals (d~γ,NO\tilde{d}_{γ,\mathrm{NO}}) and its effect on the active space size and the metric. The proposed diagnostic can also be applied to other wavefunction approximations, and it has the potential to provide a quality measure for post-Hartree-Fock procedures in general.

Reduced basis solvers for unfitted methods on parameterized domains

Authors: Nicholas Mueller, Santiago Badia, Yiran Zhao

arXiv ID: 2508.15320 | Date: 2025-08-21

Abstract: In this paper, we present a unified framework for reduced basis approximations of parametrized partial differential equations defined on parameter-dependent domains. Our approach combines unfitted finite element methods with both classical and tensor-based reduced basis techniques -- particularly the tensor-train reduced basis method -- to enable efficient and accurate model reduction on general geometries. To address the challenge of reconciling geometric variability with fixed-dimensional snapshot representations, we adopt a deformation-based strategy that maps a reference configuration to each parameterized domain. Furthermore, we introduce a localization procedure to construct dictionaries of reduced subspaces and hyper-reduction approximations, which are obtained via matrix discrete empirical interpolation in our work. We extend the proposed framework to saddle-point problems by adapting the supremizer enrichment strategy to unfitted methods and deformed configurations, demonstrating that the supremizer operator can be defined on the reference configuration without loss of stability. Numerical experiments on two- and three-dimensional problems -- including Poisson, linear elasticity, incompressible Stokes and Navier-Stokes equations -- demonstrate the flexibility, accuracy and efficiency of the proposed methodology.

Matrix Product Operator Constructions for Gauge Theories in the Thermodynamic Limit

Authors: Nicholas Godfrey, Ian P. McCulloch

arXiv ID: 2508.14145 | Date: 2025-08-19

Abstract: We present a general method for simulating lattice gauge theories in low dimensions using infinite matrix product states (iMPS). A central challenge in Hamiltonian formulations of gauge theories is the unbounded local Hilbert space associated with gauge degrees of freedom. In one spatial dimension, Gauss's law permits these gauge fields to be integrated out, yielding an effective Hamiltonian with long-range interactions among matter fields. We construct efficient matrix product operator (MPO) representations of these Hamiltonians directly in the thermodynamic limit. Our formulation naturally includes background fields and θθ-terms, requiring no modifications to the standard iDMRG algorithm. This provides a broadly applicable framework for 1+1D gauge theories and can be extended to quasi-two-dimensional geometries such as infinite cylinders, where tensor-network methods remain tractable. As a benchmark, we apply our construction to the Schwinger model, reproducing expected features including confinement, string breaking, and the critical behavior at finite mass. Because the method alters only the MPO structure, it can be incorporated with little effort into a wide range of iMPS and infinite-boundary-condition algorithms, opening the way to efficient studies of both equilibrium and non-equilibrium gauge dynamics.

Many-body theory of false vacuum decay in quantum spin chains

Authors: Christian Johansen, Alessio Recati, Iacopo Carusotto, Alberto Biella

arXiv ID: 2508.13780 | Date: 2025-08-19

Abstract: In this work we theoretically investigate the false vacuum decay process in a ferromagnetic quantum spin-1/2 chain. We develop a many-body theory describing the nucleation and the coherent dynamics of true-vacuum bubbles that is analytically tractable and agrees with numerical matrix product state calculations in all parameter regimes up to intermediate times. This bosonic theory allows us to identify different regimes in the parameter space and unravel the underlying physical mechanisms. In particular, regimes that closely correspond to the cosmological false vacuum decay picture are highlighted and characterized in terms of observable quantities.

Real-time bubble nucleation and growth for false vacuum decay on the lattice

Authors: Daan Maertens, Jutho Haegeman, Karel Van Acoleyen

arXiv ID: 2508.13645 | Date: 2025-08-19

Abstract: We revisit quantum false vacuum decay for the one-dimensional Ising model, focusing on the real-time nucleation and growth of true vacuum bubbles. Via matrix product state simulations, we demonstrate that for a wide range of parameters, the full time-dependent quantum state is well described by a Gaussian ansatz in terms of domain wall operators, with the associated vacuum bubble wave function evolving according to the linearized time-dependent variational principle. The emerging picture shows three different stages of evolution: an initial nucleation of small bubbles, followed by semi-classical bubble growth, which in turn is halted by the lattice phenomenon of Bloch oscillations. Furthermore, we find that the resonant bubble only plays a significant role in a certain region of parameter-space. However, when significant, it does lead to an approximately constant decay rate during the intermediate stage. Moreover, this rate is in quantitative agreement with the analytical result of Rutkevich (Phys. Rev. B 60, 14525) for which we provide an independent derivation based on the Gaussian ansatz.

Autoregressive Typical Thermal States

Authors: Tarun Advaith Kumar, Leon Balents, Timothy H. Hsieh, Roger G. Melko

arXiv ID: 2508.13455 | Date: 2025-08-19

Abstract: A variety of generative neural networks recently adopted from machine learning have provided promising strategies for studying quantum matter. In particular, the success of autoregressive models in natural language processing has motivated their use as variational ansätze, with the hope that their demonstrated ability to scale will transfer to simulations of quantum many-body systems. In this paper, we introduce an autoregressive framework to calculate finite-temperature properties of a quantum system based on the imaginary-time evolution of an ensemble of pure states. We find that established approaches based on minimally entangled typical thermal states (METTS) have numerical instabilities when an autoregressive recurrent neural network is used as the variational ansätz. We show that these instabilities can be mitigated by evolving the initial ensemble states with a unitary operation, along with applying a threshold to curb runaway evolution of ensemble members. By comparing our algorithm to exact results for the spin 1/2 quantum XY chain, we demonstrate that autoregressive typical thermal states are capable of accurately calculating thermal observables.

SO(n) Affleck-Kennedy-Lieb-Tasaki states as conformal boundary states of integrable SU(n) spin chains

Authors: Yueshui Zhang, Ying-Hai Wu, Meng Cheng, Hong-Hao Tu

arXiv ID: 2508.13114 | Date: 2025-08-18

Abstract: We construct a class of conformal boundary states in the SU(n)1\mathrm{SU}(n)_1 Wess-Zumino-Witten (WZW) conformal field theory (CFT) using the symmetry embedding Spin(n)2SU(n)1\mathrm{Spin}(n)_2 \subset \mathrm{SU}(n)_1. These boundary states are beyond the standard Cardy construction and possess SO(n)\mathrm{SO}(n) symmetry. The SU(n)\mathrm{SU}(n) Uimin-Lai-Sutherland (ULS) spin chains, which realize the SU(n)1\mathrm{SU}(n)_1 WZW model on the lattice, allow us to identify these boundary states as the ground states of the SO(n)\mathrm{SO}(n) Affleck-Kennedy-Lieb-Tasaki spin chains. Using the integrability of the SU(n)\mathrm{SU}(n) ULS model, we analytically compute the corresponding Affleck-Ludwig boundary entropy using exact overlap formulas. Our results unveil intriguing connections between exotic boundary states in CFT and integrable lattice models, thus providing deep insights into the interplay of symmetry, integrability, and boundary critical phenomena.

Generalized Symmetries From Fusion Actions

Authors: Chongying Dong, Siu-Hung Ng, Li Ren, Feng Xu

arXiv ID: 2508.13063 | Date: 2025-08-18

Abstract: Let AA be a condensable algebra in a modular tensor category C\mathcal{C}. We define an action of the fusion category CA\mathcal{C}_A of AA-modules in C\mathcal{C} on the morphism space HomC(x,A)_{\mathcal{C}}(x,A) for any xx in C\mathcal{C}, whose characters are generalized Frobenius-Schur indicators. This fusion action can be considered on AA, and we prove a categorical generalization of Schur-Weyl duality for this action. For any fusion subcategory B\mathcal{B} of CA\mathcal{C}_A containing all the local AA-modules, we prove the invariant subobject B=ABB=A^\mathcal{B} is a condensable subalgebra of AA. The assignment of B\mathcal{B} to ABA^\mathcal{B} defines a Galois correspondence between this kind of fusion subcategories of CA\mathcal{C}_A and the condensable subalgebras of AA. In the context of VOA, we prove for any nice VOAs UAU \subset A, U=ACAU=A^{\mathcal{C}_A} where C=MU\mathcal{C}=\mathcal{M}_U is the UU-module category. In particular, if U=AGU = A^G for some finite automorphism group GG of A,A, the fusion action of CA\mathcal{C}_A on AA is equivalent to the GG-action on A.A.

Computing Exchange Coupling constants in Transition metal complexes with Tensor Product Selected Configuration Interaction

Authors: Arnab Bachhar, Nicholas J. Mayhall

arXiv ID: 2508.13002 | Date: 2025-08-18

Abstract: Transition metal complexes present significant challenges for electronic structure theory due to strong electron correlation arising from partially filled dd-orbitals. We compare our recently developed Tensor Product Selected Configuration Interaction (TPSCI) with Density Matrix Renormalization Group (DMRG) for computing exchange coupling constants in six transition metal systems, including dinuclear Cr, Fe, and Mn complexes and a tetranuclear Ni-cubane. TPSCI uses a locally correlated tensor product state basis to capture electronic structure efficiently while maintaining interpretability. From calculations on active spaces ranging from (22e,29o) to (42e,49o), we find that TPSCI consistently yields higher variational energies than DMRG due to truncation of local cluster states, but provides magnetic exchange coupling constants (J) generally within 10-30 cm1^{-1} of DMRG results. Key advantages include natural multistate capability enabling direct J extrapolation with smaller statistical errors, and computational efficiency for challenging systems. However, cluster state truncation represents a fundamental limitation requiring careful convergence testing, particularly for large local cluster dimensions. We identify specific failure cases where current truncation schemes break down, highlighting the need for improved cluster state selection methods and distributed memory implementations to realize TPSCI's full potential for strongly correlated systems.

Quantum State Preparation by Improved MPS Method

Authors: Chao Wang, Pengrui Zhou, Xi-Ning Zhuang, Ziwei Cui, Menghan Dou, Zhao-Yun Chen, Guo-Ping Guo

arXiv ID: 2508.12821 | Date: 2025-08-18

Abstract: Efficient encoding of classical information plays a fundamental role in numerous practical quantum algorithms. However, the preparation of an arbitrary amplitude-encoded state has been proven to be time-consuming, and its deployment on current noisy devices can be challenging. In this work, we propose an improved Matrix Product State(MPS) method preparation protocol with an exponential reduction on the circuit depth, as well as topological adaptability. By refined utilization of the disentangling principle, we also reduce approximately 33% two-qubit gate count. To validate our method, we study various families of functions and distributions with provably bounded MPS rank. Numerical experiments show that our method significantly reduces circuit depth while achieving higher fidelity for states arising in financial and other applications.

Constructing Invariant and Equivariant Operations by Symmetric Tensor Network

Authors: Meng Zhang, Chao Wang, Hao Zhang, Shaojun Dong, Lixin He

arXiv ID: 2508.12596 | Date: 2025-08-18

Abstract: Design of neural networks that incorporate symmetry is crucial for geometric deep learning. Central to this effort is the development of invariant and equivariant operations. This works presents a systematic method for constructing valid invariant and equivariant operations. It can handle inputs and outputs in the form of Cartesian tensors with different rank, as well as spherical tensors with different types. In addition, our method features a graphical representation utilizing the symmetric tensor network, which simplifies both the proofs and constructions related to invariant and equivariant functions. We also apply this approach to design the equivariant interaction message for the geometry graph neural network, and equivariant machine learning model to learn the constitutive law of materials.

Simulating Quantum Turbulence with Matrix Product States

Authors: Felipe Gómez-Lozada, Nicolas Perico-García, Nikita Gourianov, Hayder Salman, Juan José Mendoza-Arenas

arXiv ID: 2508.12191 | Date: 2025-08-17

Abstract: Quantum turbulence spans length scales from the system size LL to the healing length ξξ, making direct numerical simulations (DNS) of the Gross-Pitaevskii (GP) equation computationally expensive when LξL \gg ξ. We present a matrix product state (MPS) solver for the GP equation that efficiently compresses the wavefunction by truncating weak interlength-scale correlations. This approach reduces memory usage by factors ranging from 10x to over 10,000x compared to DNS. We benchmark our approach on nonlinear excitations, namely dark solitons (1D) and quantized vortices (2D, 3D), capturing key dynamics such as Kelvin wave propagation and vortex ring emission in the case of vortex line reconnection. For turbulent states composed of multiple nonlinear excitations, we find that the memory compression of the MPS representation is directly proportional to the soliton or vortex densities. We also accurately reproduce established results from two-point correlation functions and energy spectra, where we recover the incompressible kinetic energy spectrum with little memory overhead. These results demonstrate the representative capabilities of the MPS ansatz for quantum turbulence and pave the way for studying this nonequilibrium state using previously-prohibited system sizes to uncover novel physics.

AdaRing: Towards Ultra-Light Vision-Language Adaptation via Cross-Layer Tensor Ring Decomposition

Authors: Ying Huang, Yuanbin Man, Wenqi Jia, Zhengzhong Tu, Junzhou Huang, Miao Yin

arXiv ID: 2508.11870 | Date: 2025-08-16

Abstract: Adapter-based fine-tuning has gained remarkable attention in adapting large pre-trained vision language models (VLMs) for a wide range of downstream tasks efficiently. In this paradigm, only the inserted adapters are fine-tuned, without the need for training the original VLM backbone. Existing works scale adapters by integrating them into every layer of VLMs to increase the capacity of adapters. However, these methods face two primary limitations: 1) limited compression rate due to ignoring cross-layer redundancy, and 2) limited representational capacity across homogeneous adapters. In this paper, we propose a novel vision-language fine-tuning framework based on cross-layer tensor ring decomposition (TRD) with the integration and collaboration of diverse adapters, called AdaRing, achieving ultra-light parameter-efficient adaptation of VLMs on various tasks. To remove the high redundancy that exists among adapters across layers, we exploit the tensor-level low-rankness to formulate adapters as layer-shared tensor cores and layer-specific slices. Moreover, guided by generalization-aware fine-tuning, diverse rank-driven adapters cooperate to handle tasks that require different representations. Our experiments show that the proposed AdaRing achieves the state-of-the-art performance while reducing average training parameters by 90%.

Fermi-liquid-like phase driven by next-nearest-neighbor couplings in a lightly doped kagome-lattice tt-JJ model

Authors: Xu-Yan Jia, Fan Yang, D. N. Sheng, Shou-Shu Gong

arXiv ID: 2508.11322 | Date: 2025-08-15

Abstract: Due to the interplay between charge fluctuation and geometry frustration, the doped kagome-lattice Mott insulator is a fascinating platform to realize exotic quantum states. Through the state-of-the-art density matrix renormalization group calculation, we explore the quantum phases of the lightly doped kagome-lattice tt-JJ model in the presence of the next-nearest-neighbor electron hopping t2t_2 and spin interaction J2J_2. On the Ly=3L_y = 3 cylinder (LyL_y is the number of unit cells along the circumference direction), we establish a quantum phase diagram with tuning t2>0t_2 > 0 and J2>0J_2 > 0, showing an emergent Fermi-liquid-like phase driven by increased t2t_2 and J2J_2, which sits at the neighbor of the previously identified charge density wave (CDW) phase. Compared with the CDW phase, the charge order is significantly suppressed in the Fermi-liquid-like phase, and most correlation functions are greatly enhanced with power-law decay. In particular, we find the absence of hole pairing and a strong three-sublattice magnetic correlation. On the wider Ly=4L_y = 4 cylinder, this Fermi-liquid-like phase persists at low doping levels, strongly suggesting that this state might be stable in the two-dimensional kagome system.

Goal-Oriented Low-Rank Tensor Decompositions for Numerical Simulation Data

Authors: Daniel M. Dunlavy, Eric T. Phipps, Hemanth Kolla, John N. Shadid, Edward Phillips

arXiv ID: 2508.11139 | Date: 2025-08-15

Abstract: We introduce a new low-dimensional model of high-dimensional numerical simulation data based on low-rank tensor decompositions. Our new model aims to minimize differences between the model data and simulation data as well as functions of the model data and functions of the simulation data. This novel approach to dimensionality reduction of simulation data provides a means of directly incorporating quantities of interests and invariants associated with conservation principles associated with the simulation data into the low-dimensional model, thus enabling more accurate analysis of the simulation without requiring access to the full set of high-dimensional data. Computational results of applying this approach to two standard low-rank tensor decompositions of data arising from simulation of combustion and plasma physics are presented.

Spontaneously Broken Non-Invertible Symmetries in Transverse-Field Ising Qudit Chains

Authors: Kristian Tyn Kai Chung, Umberto Borla, Andriy H. Nevidomskyy, Sergej Moroz

arXiv ID: 2508.11003 | Date: 2025-08-14

Abstract: \usepackage{iopams} Recent developments have revealed that symmetries need not form a group, but instead can be non-invertible. Here we use analytical arguments and numerical evidence to illuminate how spontaneous symmetry breaking of a non-invertible symmetry is similar yet distinct from ordinary, invertible, symmetry breaking. We consider one-dimensional chains of group-valued qudits, whose local Hilbert space is spanned by elements of a finite group GG (reducing to ordinary qubits when G=Z2G=\mathbb{Z}_2). We construct Ising-type transverse-field Hamiltonians with Rep(GG) symmetry whose generators multiply according to the tensor product of irreducible representations (irreps) of the group GG. For non-Abelian GG, the symmetry is non-invertible. In the symmetry broken phase there is one ground state per irrep on a closed chain. The symmetry breaking can be detected by local order parameters but, unlike the invertible case, different ground states have distinct entanglement patterns. We show that for each irrep of dimension greater than one the corresponding ground state exhibits string order, entanglement spectrum degeneracies, and has gapless edge modes on an open chain -- features usually associated with symmetry-protected topological order. Consequently, domain wall excitations behave as one-dimensional non-Abelian anyons with non-trivial internal Hilbert spaces and fusion rules. Our work identifies properties of non-invertible symmetry breaking that existing quantum hardware can probe.

Random Permutation Circuits are Quantum Chaotic

Authors: Bruno Bertini, Katja Klobas, Pavel Kos, Daniel Malz

arXiv ID: 2508.10890 | Date: 2025-08-14

Abstract: Random permutation circuits were recently introduced as minimal models for local many-body dynamics that can be interpreted both as classical and quantum. Standard indicators of chaos such as damage spreading, show that these systems exhibit sensitivity to initial conditions in the classical setting. Here, we address their quantum chaoticity by studying the time evolution of local operator entanglement (LOE). We show that the behaviour of LOE in random permutation circuits depends on the dimension of the local configuration space q. When q = 2, i.e. the circuits act on qubits, random permutations are Clifford and the LOE of any local operator is bounded by a constant, indicating that they are not truly chaotic. On the other hand, when the dimension of the local configuration space exceeds two, the LOE grows linearly in time. We prove this in the limit of large dimensions and present numerical evidence that a three-dimensional local configuration space is sufficient for a linear growth of LOE. Our findings highlight that quantum chaos can be produced by essentially classical dynamics. Moreover, we show that LOE can be defined also in the classical realm and put it forward as a universal indicator chaos, both quantum and classical.

QB Ground State Energy Estimation Benchmark

Authors: Nicole Bellonzi, Joshua T. Cantin, Mohammad Reza Jangrouei, Alexander Kunitsa, Jason Necaise, Nam Nguyen, John Penuel, Maxwell D. Radin, Jhonathan Romero Fontalvo, Rashmi Sundareswara, Linjun Wang, Thomas Watts, Yanbing Zhou, Michael C. Garrett, Adam Holmes, Artur F. Izmaylov, Matthew Otten

arXiv ID: 2508.10873 | Date: 2025-08-14

Abstract: Ground State Energy Estimation (GSEE) is a central problem in quantum chemistry and condensed matter physics, demanding efficient algorithms to solve complex electronic structure calculations. This work introduces a structured benchmarking framework for evaluating the performance of both classical and quantum solvers on diverse GSEE problem instances. We assess three prominent methods -- Semistochastic Heat-Bath Configuration Interaction (SHCI), Density Matrix Renormalization Group (DMRG), and Double-Factorized Quantum Phase Estimation (DF QPE) -- ighlighting their respective strengths and limitations. Our results show that fully optimized SHCI achieves near-universal solvability on the benchmark set, DMRG excels for low-entanglement systems, and DF QPE is currently constrained by hardware and algorithmic limitations. However, we observe that many benchmark Hamiltonians are drawn from datasets tailored to SHCI and related approaches, introducing a bias that favors classical solvers. To mitigate this, we propose expanding the benchmark suite to include more challenging, strongly correlated systems to enable a more balanced and forward-looking evaluation of solver capabilities. As quantum hardware and algorithms improve, this benchmarking framework will serve as a vital tool for tracking progress and identifying domains where quantum methods may surpass classical techniques. The QB-GSEE benchmark repository is openly available at https://github.com/isi-usc-edu/qb-gsee-benchmark [1]. By maintaining a scalable and open resource, we aim to accelerate innovation in computational quantum chemistry and quantum computing.

Gauging the variational optimization of projected entangled-pair states

Authors: Wei Tang, Laurens Vanderstraeten, Jutho Haegeman

arXiv ID: 2508.10822 | Date: 2025-08-14

Abstract: Projected entangled-pair states (PEPS) constitute a powerful variational ansatz for capturing ground state physics of two-dimensional quantum systems. However, accurately computing and minimizing the energy expectation value remains challenging, in part because the impact of the gauge degrees of freedom that are present in the tensor network representation is poorly understood. We analyze the role of gauge transformations for the case of a U(1)-symmetric PEPS with point group symmetry, thereby reducing the gauge degrees of freedom to a single class. We show how gradient-based optimization strategies exploit the gauge freedom, causing the tensor network contraction to become increasingly inaccurate and to produce artificially low variational energies. Furthermore, we develop a gauge-fixed optimization strategy that largely suppresses this effect, resulting in a more robust optimization. Our study underscores the need for gauge-aware optimization strategies to guarantee reliability of variational PEPS in general settings.

Edge Reconstruction in a Quantum Spin Hall Insulator

Authors: Rahul Soni, Matthias Thamm, Gonzalo Alvarez, Bernd Rosenow, Adrian Del Maestro

arXiv ID: 2508.10726 | Date: 2025-08-14

Abstract: We study interaction-driven edge reconstruction in a quantum spin Hall insulator described by the Bernevig-Hughes-Zhang model with Kanamori-Hubbard interactions using the real-space density matrix renormalization group method in both the grand-canonical and canonical ensembles. For a two-dimensional cylinder with a smooth edge, we identify discrete particle-number transitions that lead to a spin-polarized edge state stabilized by an emergent ferromagnetic exchange interaction. The reconstruction is orbital-selective, occurring predominantly in the ss-orbital channel. Our results reveal a fully microscopic mechanism for emergent spin polarization at the edge that could compromise the topological protection of helical edge states by time reversal symmetry.

Gapped spinful phases obtained via Gutzwiller projections of Euler states

Authors: Thorsten B. Wahl, Lukas Devos, Robert-Jan Slager

arXiv ID: 2508.10957 | Date: 2025-08-14

Abstract: Gutzwiller projections of non-interacting chiral topological phases are known to give rise to fractional, topologically ordered chiral phases. Here, we carry out a similar construction using two copies of non-interacting Euler insulators to produce a class of spinful interacting Euler models. To that end, we take advantage of the recently discovered exact representation of certain Euler insulators by a projected entangled pair state (PEPS) of bond dimension D=2D = 2. The Gutzwiller projection can be implemented within the tensor network formalism, giving rise to a new PEPS of bond dimension D=4D = 4. We, moreover, apply very recent state-of-the-art tensor network tools to evaluate these phases. In particular, we analyze its entanglement entropy scaling and find no topological correction to the area law, indicating that the state is not intrinsically topologically ordered. Its entanglement spectrum shows a clear cusp at momentum zero, similar to non-interacting Euler insulators, and the spectrum of the transfer operator indicates that the state is gapped, which could imply non-intrinsic topological features. Finally, the static structure factor displays Bragg peaks, indicating the simultaneous presence of local order.

Variational boundary based tensor network renormalization group

Authors: Feng-Feng Song, Naoki Kawashima

arXiv ID: 2508.10418 | Date: 2025-08-14

Abstract: We propose a real-space renormalization group algorithm for accurately coarse-graining two-dimensional tensor networks. The central innovation of our method lies in utilizing variational boundary tensors as a globally optimized environment for the entire system. Based on this optimized environment, we construct renormalization projectors that significantly enhance accuracy. By leveraging the canonical form of tensors, our algorithm maintains the same computational complexity as the original tensor renormalization group (TRG) method, yet achieves higher accuracy than existing approaches that do not incorporate entanglement filtering. Our work offers a practical pathway for extending TRG methods to higher dimensions while keeping computational costs manageable.

Quantum circuit simulation with a local time-dependent variational principle

Authors: Aaron Sander, Maximilian Fröhlich, Mazen Ali, Martin Eigel, Jens Eisert, Michael Hintermüller, Christian B. Mendl, Richard M. Milbradt, Robert Wille

arXiv ID: 2508.10096 | Date: 2025-08-13

Abstract: Classical simulations of quantum circuits are vital for assessing potential quantum advantage and benchmarking devices, yet they require sophisticated methods to avoid the exponential growth of resources. Tensor network approaches, in particular matrix product states (MPS) combined with the time-evolving block decimation (TEBD) algorithm, currently dominate large-scale circuit simulations. These methods scale efficiently when entanglement is limited but suffer rapid bond dimension growth with increasing entanglement and handle long-range gates via costly SWAP insertions. Motivated by the success of the time-dependent variational principle (TDVP) in many-body physics, we reinterpret quantum circuits as a series of discrete time evolutions, using gate generators to construct an MPS-based circuit simulation via a local TDVP formulation. This addresses TEBD's key limitations by (1) naturally accommodating long-range gates and (2) optimally representing states on the MPS manifold. By diffusing entanglement more globally, the method suppresses local bond growth and reduces memory and runtime costs. We benchmark the approach on five 49-qubit circuits: three Hamiltonian circuits (1D open and periodic Heisenberg, 2D 7x7 Ising) and two algorithmic ones (quantum approximate optimization, hardware-efficient ansatz). Across all cases, our method yields substantial resource reductions over standard tools, establishing a new state-of-the-art for circuit simulation and enabling advances across quantum computing, condensed matter, and beyond.

TensorKit.jl: A Julia package for large-scale tensor computations, with a hint of category theory

Authors: Lukas Devos, Jutho Haegeman

arXiv ID: 2508.10076 | Date: 2025-08-13

Abstract: TensorKit.jl is a Julia-based software package for tensor computations, especially focusing on tensors with internal symmetries. This paper introduces the design philosophy, core functionalities, and distinctive features, including how to handle abelian, non-abelian, and anyonic symmetries through the ``TensorMap'' type. We highlight the software's flexibility, performance, and its capability to extend to new tensor types and symmetries, illustrating its practical applications through select case studies.

Tensor-network formulation of QCD in the strong-coupling expansion

Authors: Thomas Samberger, Jacques Bloch, Robert Lohmayer, Tilo Wettig

arXiv ID: 2508.09891 | Date: 2025-08-13

Abstract: We present a tensor-network formulation for the strong-coupling expansion of QCD with staggered quarks at non-zero chemical potential, for arbitrary number of dimensions, colors, and flavors. We integrate out the gauge and quark degrees of freedom and rewrite the partition function as the complete trace of a tensor network. This network consists of local tensors that contain a numerical and a Grassmann part. We truncate the initial tensor at a fixed order in the inverse coupling ββ and compute analytical results for the partition function, the free energy, and the chiral condensate on a 2×22\times2 lattice up to order β4β^4. In a follow-up paper we will introduce an enhanced tensor-network method, order-separated GHOTRG, to explicitly compute the expansion coefficients of the partition function for larger lattices.

Entropy Measures for Transition Matrices in Random Systems

Authors: Zhaohui Chen, Rene Meyer, Zhuo-Yu Xian

arXiv ID: 2508.09261 | Date: 2025-08-12

Abstract: A transition matrix can be constructed through the partial contraction of two given quantum states. We analyze and compare four different definitions of entropy for transition matrices, including (modified) pseudo entropy, SVD entropy, and ABB entropy. We examine the probabilistic interpretation of each entropy measure and show that only the distillation interpretation of ABB entropy corresponds to the joint success probability of distilling entanglement between the two quantum states used to construct the transition matrix. Combining the transition matrix with preceding measurements and subsequent non-unitary operations, the ABB entropy either decreases or remains unchanged, whereas the pseudo-entropy and SVD entropy may increase or decrease. We further apply these entropy measures to transition matrices constructed from several ensembles: (i) pairs of independent Haar-random states; (ii) bi-orthogonal eigenstates of non-Hermitian random systems; and (iii) bi-orthogonal states in PTPT-symmetric systems near their exceptional points. Across all cases considered, the SVD and ABB entropies of the transition matrix closely mirror the behavior of the subsystem entanglement entropy of a single random state, in contrast to the (modified) pseudo entropy, which can exceed the bound of subsystem size, fail to scale with system size, or even take complex values.

Robust quantum computational advantage with programmable 3050-photon Gaussian boson sampling

Authors: Hua-Liang Liu, Hao Su, Si-Qiu Gong, Yi-Chao Gu, Hao-Yang Tang, Meng-Hao Jia, Qian Wei, Yukun Song, Dongzhou Wang, Mingyang Zheng, Faxi Chen, Libo Li, Siyu Ren, Xuezhi Zhu, Meihong Wang, Yaojian Chen, Yanfei Liu, Longsheng Song, Pengyu Yang, Junshi Chen, Hong An, Lei Zhang, Lin Gan, Guangwen Yang, Jia-Min Xu, Yu-Ming He, Hui Wang, Han-Sen Zhong, Ming-Cheng Chen, Xiao Jiang, Li Li, Nai-Le Liu, Yu-Hao Deng, Xiao-Long Su, Qiang Zhang, Chao-Yang Lu, Jian-Wei Pan

arXiv ID: 2508.09092 | Date: 2025-08-12

Abstract: The creation of large-scale, high-fidelity quantum computers is not only a fundamental scientific endeavour in itself, but also provides increasingly robust proofs of quantum computational advantage (QCA) in the presence of unavoidable noise and the dynamic competition with classical algorithm improvements. To overcome the biggest challenge of photon-based QCA experiments, photon loss, we report new Gaussian boson sampling (GBS) experiments with 1024 high-efficiency squeezed states injected into a hybrid spatial-temporal encoded, 8176-mode, programmable photonic quantum processor, Jiuzhang 4.0, which produces up to 3050 photon detection events. Our experimental results outperform all classical spoofing algorithms, particularly the matrix product state (MPS) method, which was recently proposed to utilise photon loss to reduce the classical simulation complexity of GBS. Using the state-of-the-art MPS algorithm on the most powerful supercomputer EI Capitan, it would take > 104210^{42} years to construct the required tensor network for simulation, while our Jiuzhang 4.0 quantum computer takes 25.6 μμs to produce a sample. This work establishes a new frontier of QCA and paves the way to fault-tolerant photonic quantum computing hardware.

Neural quantum states for emitter dynamics in waveguide QED

Authors: Tatiana Vovk, Anka Van de Walle, Hannes Pichler, Annabelle Bohrdt

arXiv ID: 2508.08964 | Date: 2025-08-12

Abstract: Quantum emitters coupled to one-dimensional waveguides constitute a paradigmatic quantum-optical platform for exploring collective phenomena in open quantum many-body systems. For appropriately spaced emitters, they realize the Dicke model, whose characteristic permutation symmetry allows for efficient exact solutions featuring superradiance. When the emitters are arbitrarily spaced, however, this symmetry is lost and general analytical solutions are no longer available. In this work, we introduce a novel numerical method to study the dynamics of such systems by extending the time-dependent neural quantum state (t-NQS) framework to open quantum systems. We benchmark our approach across a range of waveguide QED settings and compare its performance with tensor-network calculations. Our results demonstrate that the t-NQS approach is competitive with other numerical methods and highlight the potential of t-NQSs for studying open quantum many-body systems out of equilibrium.

Digital Quantum Simulation of Flat-Band and All-Bands-Flat Dynamics for Tunable Quantum Transport

Authors: Mrinal Kanti Giri, Pochung Chen

arXiv ID: 2508.08734 | Date: 2025-08-12

Abstract: Flat-band systems offer a uniquely powerful tool for quantum control in dynamics due to their characteristic feature of having a dispersionless energy band. Simulating such highly sensitive systems on current digital quantum computers is a challenging task, due to the intrinsic limitations of the noisy intermediate-scale quantum (NISQ) devices. Here we present high-fidelity digital quantum simulations of flat-band (FB) and all-bands-flat (ABF) lattices, using an advanced tensor-network-based circuit compression method. With the compressed quantum circuits, we first explore single-particle dynamics and observe two distinct behaviours: strong localization in ABF lattices and delocalization in FB lattices. By integrating FB and ABF lattices into a one-dimensional hybrid structure, we achieve controllable quantum transport, where the ABF lattice acts as a quantum switch. Extending to two-particle dynamics, we show that transport remains controllable by tuning the hopping amplitude alone, even in the presence of interactions. These results establish flat-band engineered systems as a promising pathway for scalable control of quantum transport in emerging quantum technologies, with potential applications in qubit isolation, particle trapping, and state transfer.

Instability of Nagaoka State and Quantum Phase Transition via Kinetic Frustration Control

Authors: Prakash Sharma, Yang Peng, Donna N. Sheng, Hitesh J. Changlani, Yao Wang

arXiv ID: 2508.08410 | Date: 2025-08-11

Abstract: We investigate the Nagaoka-Thouless (NT) ferromagnetic instability in the strongly interacting tt-tt' Hubbard model by continuously breaking particle-hole symmetry on a tunable square-triangular lattice geometry. We use an analytic approach to show that the fully spin-polarized state becomes unstable to a metastable spin-polaron when the kinetic frustration t/tt'/t exceeds a critical, dimension-dependent value. Large-scale density matrix renormalization group (DMRG) simulations reveal a quantum phase transition from the NT ferromagnet to a spiral spin-density wave, which evolves continuously into the Haerter-Shastry antiferromagnet in the large-frustration limit. Remarkably, this transition remains robust at low but finite hole density, making it accessible in cold-atom and moiré Hubbard platforms under strong interactions. A variational analysis further captures the instability mechanism at finite density via frustration-induced magnon band deformation.

Continuous topological phase transition between Z2\mathbb{Z}_2 topologically ordered phases

Authors: Qi Zhang, Wen-Tao Xu

arXiv ID: 2508.08376 | Date: 2025-08-11

Abstract: Topological phase transitions beyond anyon condensation remain poorly understood. A notable example is the transition between the toric code (TC) and double semion (DS) phases, which has two distinct Z2\mathbb{Z}_2 topological orders in (2 + 1)D. Previous studies reveal that the transition between them can be either first order or via an intermediate phase, thus the existence of a directly continuous transition between them remains a long-standing problem. Motivated by the fact that both phases can arise from condensing distinct anyons in the Z4\mathbb{Z}_4 topological order, we introduce a perturbed Z4\mathbb{Z}_4 quantum double (QD) model to study the TC-DS transition. We confirm the existence of a continuous (2 + 1)D XY* transition between the TC and DS phases by mapping it to a two-coupled quantum Ising model. Importantly, using the condensation order parameters and the area law coefficients of the Wilson loops, we further reveal that Z4\mathbb{Z}_4 anyons, fractionalized from the Z2\mathbb{Z}_2 topological orders, become deconfined at the transition between Z2\mathbb{Z}_2 topologically ordered phases. Our results open a path toward developing a theoretical framework for topological phase transitions beyond anyon condensation.

Quantum Circuit Complexity of Matrix-Product Unitaries

Authors: Georgios Styliaris, Rahul Trivedi, J. Ignacio Cirac

arXiv ID: 2508.08160 | Date: 2025-08-11

Abstract: Matrix-product unitaries (MPUs) are many-body unitary operators that, as a consequence of their tensor-network structure, preserve the entanglement area law in 1D systems. However, it is unknown how to implement an MPU as a quantum circuit since the individual tensors describing the MPU are not unitary. In this paper, we show that a large class of MPUs can be implemented with a polynomial-depth quantum circuit. For an NN-site MPU built from a repeated bulk tensor with open boundary, we explicitly construct a quantum circuit of polynomial depth T=O(Nα)T = O(N^α) realizing the MPU, where the constant αα depends only on the bulk and boundary tensor and not the system size NN. We show that this class includes nontrivial unitaries that generate long-range entanglement and, in particular, contains a large class of unitaries constructed from representations of CC^*-weak Hopf algebras. Furthermore, we also adapt our construction to nonuniform translationally-varying MPUs and show that they can be implemented by a circuit of depth O(NβpolyD)O(N^β \, \mathrm{poly}\, D) where β1+log2D/sminβ\le 1 + \log_2 \sqrt{D}/ s_{\min}, with DD being the bond dimension and smins_{\min} is the smallest nonzero Schmidt value of the normalized Choi state corresponding to the MPU.

Tomography-assisted noisy quantum circuit simulator using matrix product density operators

Authors: Wei-guo Ma, Yun-Hao Shi, Kai Xu, Heng Fan

arXiv ID: 2508.07610 | Date: 2025-08-11

Abstract: In recent years, efficient quantum circuit simulations incorporating ideal noise assumptions have relied on tensor network simulators, particularly leveraging the matrix product density operator (MPDO) framework. However, experiments on real noisy intermediate-scale quantum (NISQ) devices often involve complex noise profiles, encompassing uncontrollable elements and instrument-specific effects such as crosstalk. To address these challenges, we employ quantum process tomography (QPT) techniques to directly capture the operational characteristics of the experimental setup and integrate them into numerical simulations using MPDOs. Our QPT-assisted MPDO simulator is then applied to explore a variational approach for generating noisy entangled states, comparing the results with standard noise numerical simulations and demonstrations conducted on the Quafu cloud quantum computation platform. Additionally, we investigate noisy MaxCut problems, as well as the effects of crosstalk and noise truncation. Our results provide valuable insights into the impact of noise on NISQ devices and lay the foundation for enhanced design and assessment of quantum algorithms in complex noise environments.

A Method for Constructing Quasi-Random Peaked Quantum Circuits

Authors: O. G. Udalov

arXiv ID: 2508.07491 | Date: 2025-08-10

Abstract: An algorithm is proposed for constructing quasi-random "peaked" quantum circuits, i.e., circuits whose final qubit state exhibits a high probability concentration on a specific computational basis state. These circuits consist of random gates arranged in a brick-wall architecture. While the multiqubit state in the middle of the circuit can exhibit significant entanglement, the final state is, with high probability, a predetermined pure bitstring. A technique is introduced to obscure the final bitstring in the structure of the quantum circuit. The algorithm allows precise control over the probability of the final peaked state. A modified version of the algorithm enables the construction of double- or multi-peaked quantum circuits. The matrix product state (MPS) method is evaluated for simulating such circuits; it performs effectively for shallow peaked circuits but offers no significant advantage for deeper ones.

Magnetically Mediated Cross-Layer Pairing in Pressurized Trilayer Nickelate La4_4Ni3_3O10_{10}

Authors: Jialin Chen, Chuanshu Xu, Qiaoyi Li, Wei Li

arXiv ID: 2508.06802 | Date: 2025-08-09

Abstract: The recently discovered trilayer nickelate superconductor La4_4Ni3_3O10_{10} under pressure has emerged as a promising platform for exploring unconventional superconductivity. However, the pairing mechanism remains a subject of active investigations. With large-scale density matrix renormalization group calculations on a realistic two-orbital trilayer Hubbard model, we elucidate the superconducting (SC) mechanism in this system. Our results reveal distinct magnetic correlations in the two different orbitals: while the dz2d_{z^2} orbital exhibits both interlayer and cross-layer antiferromagnetic (AFM) correlations, the dx2y2d_{x^2-y^2} orbital shows exclusively cross-layer AFM correlations, rendering a quasi-long-range SC order in the latter. We demonstrate that the Hund's rule coupling is essential for forming the SC order, and discuss the effects of kinetic AFM correlation and Hubbard repulsive UU. Our findings motivate a further simplification of the trilayer Hubbard to an effective bilayer mixed-dimensional Hubbard model, providing a unified framework for understanding interlayer SC in both trilayer and bilayer nickelates.

A Tensor Train Approach for Deterministic Arithmetic Operations on Discrete Representations of Probability Distributions

Authors: Gerhard Kirsten, Bilgesu Bilgin, Janith Petangoda, Phillip Stanley-Marbell

arXiv ID: 2508.06303 | Date: 2025-08-08

Abstract: Computing with discrete representations of high-dimensional probability distributions is fundamental to uncertainty quantification, Bayesian inference, and stochastic modeling. However, storing and manipulating such distributions suffers from the curse of dimensionality, as memory and computational costs grow exponentially with dimension. Monte Carlo methods require thousands to billions of samples, incurring high computational costs and producing inconsistent results due to stochasticity. We present an efficient tensor train method for performing exact arithmetic operations on discretizations of continuous probability distributions while avoiding exponential growth. Our approach leverages low-rank tensor train decomposition to represent latent random variables compactly using Dirac deltas, enabling deterministic addition, subtraction and multiplication operations directly in the compressed format. We develop an efficient implementation using sparse matrices and specialized data structures that further enhances performance. Theoretical analysis demonstrates polynomial scaling of memory and computational complexity under rank assumptions, and shows how statistics of latent variables can be computed with polynomial complexity. Numerical experiments spanning randomized linear algebra to stochastic differential equations demonstrate orders-of-magnitude improvements in memory usage and computational time compared to conventional approaches, enabling tractable deterministic computations on discretized random variables in previously intractable dimensions.

Synthetic Data Generation and Differential Privacy using Tensor Networks' Matrix Product States (MPS)

Authors: Alejandro Moreno R., Desale Fentaw, Samuel Palmer, Raúl Salles de Padua, Ninad Dixit, Samuel Mugel, Roman Orús, Manuel Radons, Josef Menter, Ali Abedi

arXiv ID: 2508.06251 | Date: 2025-08-08

Abstract: Synthetic data generation is a key technique in modern artificial intelligence, addressing data scarcity, privacy constraints, and the need for diverse datasets in training robust models. In this work, we propose a method for generating privacy-preserving high-quality synthetic tabular data using Tensor Networks, specifically Matrix Product States (MPS). We benchmark the MPS-based generative model against state-of-the-art models such as CTGAN, VAE, and PrivBayes, focusing on both fidelity and privacy-preserving capabilities. To ensure differential privacy (DP), we integrate noise injection and gradient clipping during training, enabling privacy guarantees via Rényi Differential Privacy accounting. Across multiple metrics analyzing data fidelity and downstream machine learning task performance, our results show that MPS outperforms classical models, particularly under strict privacy constraints. This work highlights MPS as a promising tool for privacy-aware synthetic data generation. By combining the expressive power of tensor network representations with formal privacy mechanisms, the proposed approach offers an interpretable and scalable alternative for secure data sharing. Its structured design facilitates integration into sensitive domains where both data quality and confidentiality are critical.

Scalable Quantum State Preparation for Encoding Genomic Data with Matrix Product States

Authors: Floyd M. Creevey, Hitham T. Hassan, James McCafferty, Lloyd C. L. Hollenberg, Sergii Strelchuk

arXiv ID: 2508.06184 | Date: 2025-08-08

Abstract: As quantum computing hardware advances, the need for algorithms that facilitate the loading of classical data into the quantum states of these devices has become increasingly important. This study presents a method for producing scalable quantum circuits to encode genomic data using the Matrix Product State (MPS) formalism. The method is illustrated by encoding the genome of the bacteriophage ΦX174ΦX174 into a 15-qubit state, and analysing the trade-offs between MPS bond dimension, reconstruction error, and the resulting circuit complexity. This study proposes methods for optimising encoding circuits with standard benchmark datasets for the emerging field of quantum bioinformatics. The results for circuit generation and simulation on HPC and on current quantum hardware demonstrate the viability and utility of the encoding.

Diagonalizing large-scale quantum many-body Hamiltonians using variational quantum circuit and tensor network

Authors: Peng-Fei Zhou, Shuang Qiao, An-Chun Ji, Shi-Ju Ran

arXiv ID: 2508.06159 | Date: 2025-08-08

Abstract: Exact diagonalization (ED) is an essential tool for exploring quantum many-body physics but is fundamentally limited by the exponentially-scaled computational complexity. Here, we propose tensor network variational diagonalization (TNVD), which encodes the full eigenenergy spectrum of a quantum many-body Hamiltonian into a matrix product state, and encodes the eigenstates as the evolutions of product states using variational quantum circuit (VQC). Thereby, TNVD reduces the computational complexity of diagonalization from exponential to polynomial in system size NN. Numerical benchmarks up to N=100N=100 spins are provided, which far surpass the computational limit of ED. We further consider quantum Ising model in a random field to reveal the underlying reliance between the efficiency of TNVD and entanglement properties of eigenstates. Typical signs, including the distribution of entanglement entropy (EE) versus eigenenergy and the density of state versus EE, are suggested to indicate area law of entanglement entropy or its violation, which are essential to the TNVD efficiency. Our work establishes TNVD as a powerful and scalable diagonalization approach for large-scale quantum many-body Hamiltonians. The incorporation of VQC lays a promising pathway to applying quantum computation to address the volume-law-EE Hamiltonians that lack efficient classical approaches.

MPS-JuliQAOA: User-friendly, Scalable MPS-based Simulation for Quantum Optimization

Authors: Sean Feeney, Reuben Tate, John Golden, Stephan Eidenbenz

arXiv ID: 2508.05883 | Date: 2025-08-07

Abstract: We present the MPS-JuliQAOA simulator, a user-friendly, open-source tool to simulate the Quantum Approximate Optimization Algorithm (QAOA) of any optimization problem that can be expressed as diagonal Hamiltonian. By leveraging Julia-language constructs and the ITensor package to implement a Matrix Product State (MPS) approach to simulating QAOA, MPS-Juli-QAOA effortlessly scales to 512 qubits and 20 simulation rounds on the standard de-facto benchmark 3-regular MaxCut QAOA problem. MPS-JuliQAOA also has built-in parameter finding capabilities, which is a crucial performance aspect of QAOA. We illustrate through examples that the user does not need to know MPS principles or complex automatic differentiation techniques to use MPS-JuliQAOA. We study the scalability of our tool with respect to runtime, memory usage and accuracy tradeoffs. Code available at https://github.com/lanl/JuliQAOA.jl/tree/mps.

Classical simulation of noisy quantum circuits via locally entanglement-optimal unravelings

Authors: Simon Cichy, Paul K. Faehrmann, Lennart Bittel, Jens Eisert, Hakop Pashayan

arXiv ID: 2508.05745 | Date: 2025-08-07

Abstract: Classical simulations of noisy quantum circuits is instrumental to our understanding of the behavior of real world quantum systems and the identification of regimes where one expects quantum advantage. In this work, we present a highly parallelizable tensor-network-based classical algorithm -- equipped with rigorous accuracy guarantees -- for simulating nn-qubit quantum circuits with arbitrary single-qubit noise. Our algorithm represents the state of a noisy quantum system by a particular ensemble of matrix product states from which we stochastically sample. Each single qubit noise process acting on a pure state is then represented by the ensemble of states that achieve the minimal average entanglement (the entanglement of formation) between the noisy qubit and the remainder. This approach lets us use a more compact representation of the quantum state for a given accuracy requirement and noise level. For a given maximum bond dimension χχ and circuit, our algorithm comes with an upper bound on the simulation error, runs in poly(n,χ)(n,χ)-time and improves upon related prior work (1) in scope: by extending from the three commonly considered noise models to general single qubit noise (2) in performance: by employing a state-dependent locally-entanglement-optimal unraveling and (3) in conceptual contribution: by showing that the fixed unraveling used in prior work becomes equivalent to our choice of unraveling in the special case of depolarizing and dephasing noise acting on a maximally entangled state.

Role of Plaquette Term in Genuine 2+12+1D String Dynamics on Quantum Simulators

Authors: Yizhuo Tian, N. S. Srivatsa, Kaidi Xu, Jesse J. Osborne, Umberto Borla, Jad C. Halimeh

arXiv ID: 2508.05736 | Date: 2025-08-07

Abstract: With the advent of quantum simulators of 2+12+1D lattice gauge theories (LGTs), a fundamental open question is under what circumstances the observed physics is genuinely 2+12+1D rather than effectively 1+11+1D. Here, we address this question in the ongoing strong effort to quantum-simulate string dynamics in 2+12+1D LGTs on state-of-the-art quantum hardware. Through tensor network simulations and analytic derivations, we show that the plaquette term, which represents a magnetic field and only emerges in d>1d>1 spatial dimensions, plays a crucial role in \textit{genuine} 2+12+1D string dynamics deep in the confined regime. In its absence and for minimal-length (Manhattan-distance) strings, we demonstrate how string breaking, although on a lattice in d=2d=2 spatial dimensions, can be effectively mapped to a 1+11+1D dynamical process independently of lattice geometry. Our findings not only answer the question of what qualifies as genuine 2+12+1D string dynamics, but also serve as a clear guide for future quantum simulation experiments of 2+12+1D LGTs.

Partial projected ensembles and spatiotemporal structure of information scrambling

Authors: Saptarshi Mandal, Pieter W. Claeys, Sthitadhi Roy

arXiv ID: 2508.05632 | Date: 2025-08-07

Abstract: Thermalisation and information scrambling in out-of-equilibrium quantum many-body systems are deeply intertwined: local subsystems dynamically approach thermal density matrices while their entropies track information spreading. Projected ensembles--ensembles of pure states conditioned on measurement outcomes of complementary subsystems--provide higher-order probes of thermalisation, converging at late times to universal maximum-entropy ensembles. In this work, we introduce the partial projected ensemble (PPE) as a framework to study how the spatiotemporal structure of scrambling is imprinted on projected ensembles. The PPE consists of an ensemble of mixed states induced on a subsystem by measurements on a spatially separated part of its complement, tracing out the remainder, naturally capturing scenarios involving discarded outcomes or noise-induced losses. We show that statistical fluctuations of the PPE faithfully track the causal lightcone of information spreading, revealing how scrambling dynamics are encoded in ensemble structure. In addition, we demonstrate that the probabilities of bit-string probabilities (PoPs) associated with the PPE exhibit distinct dynamical regimes and provide an experimentally accessible probe of scrambling. Both PPE fluctuations and PoPs display exponential sensitivity to the size of the discarded region, reflecting exponential degradation of quantum correlations under erasure. We substantiate these findings using the non-integrable kicked Ising chain, combining numerics in the ergodic regime with exact results at its self-dual point. We extend our analysis to a many-body localised (MBL) regime numerically, along with analytic results for the \ell-bit model. The linear and logarithmic lightcones characteristic of ergodic and MBL regimes emerge naturally from PPE dynamics, establishing it as a powerful tool for probing scrambling and deep thermalisation.

Symmetry Resolved Entanglement Entropy in a Non-Abelian Fractional Quantum Hall State

Authors: Mark J. Arildsen, Valentin Crépel, Nicolas Regnault, Benoit Estienne

arXiv ID: 2508.05494 | Date: 2025-08-07

Abstract: Symmetry-resolved entanglement entropy provides a powerful framework for probing the internal structure of quantum many-body states by decomposing entanglement into contributions from distinct symmetry sectors. In this work, we apply matrix product state techniques to study the bosonic, non-Abelian Moore-Read quantum Hall state, enabling precise numerical evaluation of both the full counting statistics and symmetry-resolved entanglement entropies. Our results reveal an approximate equipartition of entanglement among symmetry sectors, consistent with theoretical expectations and subject to finite-size corrections. The results also show that these expectations for symmetry-resolved entanglement entropy remain valid in the case of a non-Abelian state where the topological sectors cannot be distinguished by the Abelian U(1)\mathrm{U}(1) symmetry alone, and where neutral and charged modes possess distinct velocities. We additionally perform a detailed comparison of the entanglement spectrum with predictions from the Li-Haldane conjecture, finding remarkable agreement, and enabling a more precise understanding of the effects of the distinct neutral and charged velocities. This not only provides a stringent test of the conjecture but also highlights its explanatory power in understanding the origin and structure of finite-size effects across different symmetry sectors.

Global Tensor Network Renormalization for 2D Quantum systems: A new window to probe universal data from thermal transitions

Authors: Atsushi Ueda, Sander De Meyer, Adwait Naravane, Victor Vanthilt, Frank Verstraete

arXiv ID: 2508.05406 | Date: 2025-08-07

Abstract: We propose a new tensor network renormalization group (TNR) scheme based on global optimization and introduce a new method for constructing the finite-temperature density matrix of two-dimensional quantum systems. Combining these two into a new algorithm called thermal tensor network renormalization (TTNR), we obtain highly accurate conformal field theory (CFT) data at thermal transition points. This provides a new and efficient route for numerically identifying phase transitions, offering an alternative to the conventional analysis via critical exponents.

Quantum criticality and emergent orders in the spin-1 bilinear-biquadratic-Kitaev chain

Authors: Zhiling Wei, Zhengzhong Du, Xiaodong Cao, Wen-Long You, Yi Lu

arXiv ID: 2508.05216 | Date: 2025-08-07

Abstract: Higher-spin quantum magnets with competing interactions offer a rich platform for exploring quantum phases that transcend the paradigms of spin-1/2 systems, owing to their enlarged local Hilbert spaces and the emergence of multipolar correlations. We investigate a one-dimensional spin-1 chain where quadrupolar order is promoted by two distinct mechanisms: conventional bilinear-biquadratic exchange and bond-directional antiferromagnetic Kitaev frustration. Using density matrix renormalization group calculations, we determine the complete ground-state phase diagram and uncover two emergent phases induced by the Kitaev interaction: a Kitaev nematic phase and a Kitaev-dimer phase. The Kitaev nematic phase emerges from a fragile biquadratic dimer state via a continuous quantum phase transition in the Ising universality class. The Kitaev dimer phase spontaneously breaks a screw symmetry to favor either xx- or yy-spin bonding, forming a gapped state that coexists with a crystalline order of alternating Z2\mathbb{Z}_2 fluxes.

Hybrid quantum tensor networks for aeroelastic applications

Authors: M. Lautaro Hickmann, Pedro Alves, David Quero, Friedhelm Schwenker, Hans-Martin Rieser

arXiv ID: 2508.05169 | Date: 2025-08-07

Abstract: We investigate the application of hybrid quantum tensor networks to aeroelastic problems, harnessing the power of Quantum Machine Learning (QML). By combining tensor networks with variational quantum circuits, we demonstrate the potential of QML to tackle complex time series classification and regression tasks. Our results showcase the ability of hybrid quantum tensor networks to achieve high accuracy in binary classification. Furthermore, we observe promising performance in regressing discrete variables. While hyperparameter selection remains a challenge, requiring careful optimisation to unlock the full potential of these models, this work contributes significantly to the development of QML for solving intricate problems in aeroelasticity. We present an end-to-end trainable hybrid algorithm. We first encode time series into tensor networks to then utilise trainable tensor networks for dimensionality reduction, and convert the resulting tensor to a quantum circuit in the encoding step. Then, a tensor network inspired trainable variational quantum circuit is applied to solve either a classification or a multivariate or univariate regression task in the aeroelasticity domain.

Symmetry breaking and competing valence bond states in the star lattice Heisenberg antiferromagnet

Authors: Pratyay Ghosh, Jan Koziol, Samuel Nyckees, Kai Phillip Schmidt, Frédéric Mila

arXiv ID: 2508.05133 | Date: 2025-08-07

Abstract: We investigate the ground state phase diagram of the spin-1/21/2 antiferromagnetic Heisenberg model on the star lattice using infinite projected entangled pair states (iPEPS) and high-order series expansions. The model includes two distinct couplings: JdJ_d on the dimer bonds and JtJ_t on the trimer bonds. While it is established that the system hosts a valence bond solid (VBS) phase for JdJtJ_d \ge J_t, the ground state phase diagram for Jd<JtJ_d < J_t has remained unsettled. Our iPEPS simulations uncover a first-order phase transition at Jd/Jt0.18J_d/J_t \approx 0.18, significantly lower than previously reported estimates. Beyond this transition, we identify a close competition between two valence bond crystal (VBC) states: a columnar VBC and a 3×3\sqrt{3} \times \sqrt{3} VBC, with the latter consistently exhibiting lower energy across all finite bond dimensions. The high-order series expansion supports this by finding that the 3×3\sqrt{3} \times \sqrt{3} VBC state indeed becomes energetically favorable, but only at sixth order in perturbation theory, revealing the subtle nature of the competition between candidate states.

Quantum State Preparation for Medical Data: Comprehensive Methods, Implementation Challenges, and Clinical Prospects

Authors: Nikhil Kumar Rajput, Riya Bansal

arXiv ID: 2508.05063 | Date: 2025-08-07

Abstract: Quantum computing holds transformative potential for medical applications, yet efficiently preparing quantum states from complex medical data remains a fundamental challenge. This survey provides a comprehensive examination of current approaches for encoding medical information into quantum systems, analyzing theoretical principles, algorithmic advancements, and practical limitations. It discusses tensor network decomposition, variational quantum algorithms, quantum machine learning techniques, and specialized error mitigation strategies for medical computing. The findings indicate that quantum advantages in medicine rely on leveraging inherent data structures such as spatial correlations in imaging, temporal patterns in physiological signals, and hierarchical biological organization. While current hardware restricts implementations to small-scale problems, emerging methods show potential for near-term use. The study provides a structured framework for assessing when quantum state preparation outperforms classical approaches in medicine, along with implementation guidelines and performance benchmarks.

Absolutely maximally entangled pure states of multipartite quantum systems

Authors: Grzegorz Rajchel-Mieldzioć, Rafał Bistroń, Albert Rico, Arul Lakshminarayan, Karol Życzkowski

arXiv ID: 2508.04777 | Date: 2025-08-06

Abstract: Absolutely maximally entangled (AME) pure states of a system composed of NN parties are distinguished by the property that for any splitting at least one partial trace is maximally mixed. Due to maximal possible correlations between any two selected subsystems these states have numerous applications in various fields of quantum information processing including multi-user teleportation, quantum error correction and secret sharing. We present an updated survey of various techniques to generate such strongly entangled states, including those going beyond the standard construction of graph and stabilizer states. Our contribution includes, in particular, analysis of the degree of entanglement of reduced states obtained by partial trace of AME projectors, states obtained by a symmetric superposition of GHZ states, an orthogonal frequency square representation of the "golden" AME state and an updated summary of the number of local unitary equivalence classes.

Hyperbolic tiling neighborhoods in O(1) time

Authors: Yanick Thurn, Manuel Schrauth, Johanna Erdmenger

arXiv ID: 2508.04765 | Date: 2025-08-06

Abstract: Tilings of the hyperbolic plane are of significant interest among many branches of mathematics, physics and computer science. Yet, their construction remains a non-trivial task. Current approaches primarily use tree-based recursive algorithms, which are fundamentally limited: they do not readily yield the neighborhood graph representing cell adjacencies, which is however required for many applications. We introduce a novel approach that allows to build hyperbolic tilings and their associated graph structure simultaneously, using only combinatoric rules without requiring an explicit coordinate representation. This allows to generate arbitrarily large, exact hyperbolic graphs, with an algorithmic complexity that does not depend on the lattice size. We provide an easy-to-use implementation which substantially outperforms existing methods, hence rendering ultra large-scale numerical simulations on these geometric structures accessible for the scientific community.

Quantum circuit complexity and unsupervised machine learning of topological order

Authors: Yanming Che, Clemens Gneiting, Xiaoguang Wang, Franco Nori

arXiv ID: 2508.04486 | Date: 2025-08-06

Abstract: Inspired by the close relationship between Kolmogorov complexity and unsupervised machine learning, we explore quantum circuit complexity, an important concept in quantum computation and quantum information science, as a pivot to understand and to build interpretable and efficient unsupervised machine learning for topological order in quantum many-body systems. To span a bridge from conceptual power to practical applicability, we present two theorems that connect Nielsen's quantum circuit complexity for the quantum path planning between two arbitrary quantum many-body states with fidelity change and entanglement generation, respectively. Leveraging these connections, fidelity-based and entanglement-based similarity measures or kernels, which are more practical for implementation, are formulated. Using the two proposed kernels, numerical experiments targeting the unsupervised clustering of quantum phases of the bond-alternating XXZ spin chain, the ground state of Kitaev's toric code and random product states, are conducted, demonstrating their superior performance. Relations with classical shadow tomography and shadow kernel learning are also discussed, where the latter can be naturally derived and understood from our approach. Our results establish connections between key concepts and tools of quantum circuit computation, quantum complexity, and machine learning of topological quantum order.

Graphical Calculus for Fermionic Tensors

Authors: Yuanjie Ren, Kaifeng Bu, Andreas Bauer

arXiv ID: 2508.03976 | Date: 2025-08-06

Abstract: We introduce a graphical calculus, consisting of a set of fermionic tensors with tensor-network equations, which can be used to perform various computations in fermionic many-body physics purely diagrammatically. The indices of our tensors primarily correspond to fermionic modes, but also include qubits and fixed odd-parity states. Our graphical calculus extends the ZX calculus for systems involving qubits. We apply the calculus in order to represent various objects, operations, and computations in physics, including fermionic Gaussian states, the partial trace of Majorana modes, purification protocols, fermionization and bosonization maps, and the construction of fermionic codes.

Diverging conditional correlation lengths in the approach to high temperature

Authors: Jerome Lloyd, Dmitry A. Abanin, Sarang Gopalakrishnan

arXiv ID: 2508.02567 | Date: 2025-08-04

Abstract: The Markov length was recently proposed as an information-theoretic diagnostic for quantum mixed-state phase transitions [Sang & Hsieh, Phys. Rev. Lett. 134, 070403 (2025)]. Here, we show that the Markov length diverges even under classical stochastic dynamics, when a low-temperature ordered state is quenched into the high temperature phase. Conventional observables do not exhibit growing length scales upon quenching into the high-temperature phase; however, the Markov length grows exponentially in time. Consequently, the state of a system as it heats becomes increasingly non-Gibbsian, and the range of its putative "parent Hamiltonian" must diverge with the Markov length. From this information-theoretic point of view the late-time limit of thermalization is singular. We introduce a numerical technique for computing the Markov length based on matrix-product states, and explore its dynamics under general thermal quenches in the one-dimensional classical Ising model. For all cases, we provide simple information-theoretic arguments that explain our results.

Dynamical axion fields coupled with one-dimensional spinless fermions

Authors: Yuto Hosogi, Koichiro Furutani, Yuki Kawaguchi

arXiv ID: 2508.02370 | Date: 2025-08-04

Abstract: We investigate coupled dynamics of spinless fermions on a one-dimensional lattice and spins on the links. When the hopping integral and the on-site potential of the fermions depend on the direction of the link spins, the low-energy effective theory predicts that the link spins behave as a dynamical axion field in 1+1 dimensions. The axion field θθ is coupled to the electric field EE as θEθE, through which the link spins rotate in response to the applied electric field or the chemical potential gradient for charge-neutral fermions. This is the inverse phenomenon of Thouless pumping in the Rice-Mele model. After analyzing the dynamics by approximating the link spins with the classical ones and utilizing the axion Lagrangian, we show the full-quantum dynamics using the tensor network method. Even though we do not explicitly introduce the axion Lagrangian in solving the fermion-spin coupled many-body dynamics, the full-quantum results agree well with those with the classical spin approximation, including the dynamics of the axion field and fermion transport. In addition, we find that the quantum correlation between spins accelerates the dynamics of axion fields as the suppression of the expectation values of the link spins allows them to rotate easily. We also propose a possible experimental setup for cold-atomic systems to implement the Hamiltonian in this study.

Bose-Hubbard model in the canonical ensemble: a beyond mean-field approach

Authors: Tista Banerjee

arXiv ID: 2508.01692 | Date: 2025-08-03

Abstract: Ultracold atoms in optical lattices are versatile testbeds to study and manipulate equilibrium and out-of-equilibrium aspects of quantum many-body systems whose behavior can be described by Hubbard-type Hamiltonians. In this paper, we consider an ansatz wave-function which respects total particle-number conservation for such systems and goes beyond mean-field theory; this wave-function has the same complexity in the number of parameters as the mean-field Gutzwiller ansatz, and captures quantum correlations and entanglement via projection onto an effective low-energy manifold. This ansatz can be exploited to study quantum phases observed in a large class of systems realizable in such experimental platforms and is useful to study quantum dynamics. We show that the relaxation dynamics of various out-of-equilibrium initial states under sudden quench of Hamiltonian parameters can be studied with this ansatz wavefunction within the framework of time-dependent variational principle. We present a quantitative comparison with small-scale exact diagonalization results in the 1D Bose-Hubbard model with and without external trapping potentials.

Transport in Single Quantum Dots: A Review from Linear Response to Nonlinear Regimes

Authors: Gustavo Diniz, Silvio Quintino, Vivian V. França

arXiv ID: 2508.01376 | Date: 2025-08-02

Abstract: Quantum dots are versatile systems for exploring quantum transport, electron correlations, and many-body phenomena such as the Kondo effect. While equilibrium properties are well understood through methods like the numerical renormalization group and density matrix renormalization group, nonequilibrium transport remains a major theoretical challenge. From the experimental point of view, recent advances in nanofabrication and measurement techniques have enabled the investigation of far-from-equilibrium regimes. These conditions give rise to new transport phenomena, where strong correlations and nonequilibrium dynamics interplay in complex ways; beyond the reach of conventional linear response theory. To meet these challenges, new approaches such as nonequilibrium Green's functions, real-time NRG, and time-dependent DMRG have emerged. This work reviews the established results for quantum dot transport in and beyond the linear regime, highlights recent theoretical and experimental advances, and discusses open problems and future prospects.

TensorHyper-VQC: A Tensor-Train-Guided Hypernetwork for Robust and Scalable Variational Quantum Computing

Authors: Jun Qi, Chao-Han Yang, Pin-Yu Chen, Min-Hsiu Hsieh

arXiv ID: 2508.01116 | Date: 2025-08-01

Abstract: Variational Quantum Computing (VQC) faces fundamental scalability barriers, primarily due to the presence of barren plateaus and its sensitivity to quantum noise. To address these challenges, we introduce TensorHyper-VQC, a novel tensor-train (TT)-guided hypernetwork framework that significantly improves the robustness and scalability of VQC. Our framework fully delegates the generation of quantum circuit parameters to a classical TT network, effectively decoupling optimization from quantum hardware. This innovative parameterization mitigates gradient vanishing, enhances noise resilience through structured low-rank representations, and facilitates efficient gradient propagation. Grounded in Neural Tangent Kernel and statistical learning theory, our rigorous theoretical analyses establish strong guarantees on approximation capability, optimization stability, and generalization performance. Extensive empirical results across quantum dot classification, Max-Cut optimization, and molecular quantum simulation tasks demonstrate that TensorHyper-VQC consistently achieves superior performance and robust noise tolerance, including hardware-level validation on a 156-qubit IBM Heron processor. These results position TensorHyper-VQC as a scalable and noise-resilient framework for advancing practical quantum machine learning on near-term devices.

Biorthogonal Neural Network Approach to Two-Dimensional Non-Hermitian Systems

Authors: Massimo Solinas, Brandon Barton, Yuxuan Zhang, Jannes Nys, Juan Carrasquilla

arXiv ID: 2508.01072 | Date: 2025-08-01

Abstract: Non-Hermitian quantum many-body systems exhibit a rich array of physical phenomena, including non-Hermitian skin effects and exceptional points, that remain largely inaccessible to existing numerical techniques. In this work, we investigate the application of variational Monte Carlo and neural network wavefunction representations to examine their ground-state (the eigenstate with the smallest real part energy) properties. Due to the breakdown of the Rayleigh-Ritz variational principle in non-Hermitian settings, we develop a self-consistent symmetric optimization framework based on variance minimization with a dynamically updated energy estimate. Our approach respects the biorthogonal structure of left and right eigenstates, and is further strengthened by exploiting system symmetries and pseudo-Hermiticity. Tested on a two-dimensional non-Hermitian transverse field Ising model endowed with a complex longitudinal field, our method achieves high accuracy across both parity-time symmetric and broken phases. Moreover, we propose novel optimization routines that address the challenges posed by exceptional points and provide reliable convergence to the ground state in regimes where standard variational techniques fail. Lastly, we show, through extensive numerical evidence, that our method offers a scalable and flexible computational tool to investigate non-Hermitian quantum many-body systems, beyond the reach of conventional numerical techniques such as the density-matrix renormalization group algorithm.

Band mixing effects in one-dimensional charge transfer insulators

Authors: Samuel Milner, Steven Johnston, Adrian Feiguin

arXiv ID: 2508.01011 | Date: 2025-08-01

Abstract: The low-energy properties of transition metal oxides (TMOs) are governed by the electrons occupying strongly correlated dd-orbitals that are hybridized with surrounding ligand oxygen pp orbitals to varying degrees. Their physics is thus established by a complex interplay between the transition-metal (TM)-ligand hopping tt, charge transfer energy ΔCTΔ_\mathrm{CT}, and on-site TM Hubbard repulsion UU. Here, we study the spectral properties of a one-dimensional (1D) analog of such a pdpd system, with alternating TM dd and ligand anion pp orbitals situated along a chain. Using the density matrix renormalization group method, we study the model's single-particle spectral function, x-ray absorption spectrum, and dynamical spin structure factor as a function of ΔCTΔ_\mathrm{CT} and UU. In particular, we present results spanning from the Mott insulating (ΔCT>UΔ_\mathrm{CT} > U) to negative charge transfer regime ΔCT<0Δ_\mathrm{CT} < 0 to better understand the ground and momentum-resolved excited state properties of these different regimes. Our results can guide new studies on TMOs that seek to situate them within the Mott-Hubbard/charge transfer insulator classification scheme.

Truncating loopy tensor networks by zero-mode gauge fixing

Authors: Ihor Sokolov, Yintai Zhang, Jacek Dziarmaga

arXiv ID: 2508.00338 | Date: 2025-08-01

Abstract: Loopy tensor networks have internal correlations that often make their compression inefficient. We show that even local bond optimization can make better use of the insight it has locally into relevant loop correlations. By cutting the bond, we define a set of states whose linear dependence can be used to truncate the bond dimension. The linear dependence is eliminated with zero modes of the states' metric tensor. The method is illustrated by a series of examples for the infinite pair entangled projected state (iPEPS) and for the periodic matrix product state (pMPS) that occurs in the tensor renormalization group (TRG) step. In all examples, it provides better initial truncation errors than standard initialization.

Anyon superfluid in trilayer quantum Hall systems

Authors: Taige Wang, Ya-Hui Zhang

arXiv ID: 2508.00058 | Date: 2025-07-31

Abstract: Intertwining intrinsic topological order with gapless collective modes remains a central challenge in many-body physics. We show that a quantum-Hall trilayer at ν1=ν2=ν3=13ν_{1}=ν_{2}=ν_{3}= \frac13, tuned solely by the inter-layer spacing dd, realizes this goal. Large-scale density-matrix renormalization group (DMRG) calculations and a Chern-Simons field theory analysis reveal an intermediate ``anyon-exciton condensate'' separating the familiar νtot=1ν_{\mathrm{tot}}=1 exciton condensate (d0d \to 0) from three decoupled Laughlin liquids (dd \to \infty). In this phase, neutral bi-excitons condense while a ν=23ν=\frac23 Laughlin topological order survives, yielding a Goldstone mode coexisting with fractionalized anyons. A Ginzburg-Landau analysis maps out the finite-temperature phase diagram. The anyon-exciton condensate can be experimentally verified through a vanishing double-counter-flow resistance and a fractional layer-resolved Hall resistivity Rxy=52h/e2R_{xy}=\frac{5}{2} h/e^{2}, both within reach of existing high-mobility trilayer devices.

Free Independence and Unitary Design from Random Matrix Product Unitaries

Authors: Neil Dowling, Jacopo De Nardis, Markus Heinrich, Xhek Turkeshi, Silvia Pappalardi

arXiv ID: 2508.00051 | Date: 2025-07-31

Abstract: Unitary randomness underpins both fundamental tasks in quantum information and the modern theory of quantum chaos. On one side, a central concept is that of approximate unitary designs: circuits that look random according to small moments and for forward-in-time protocols. In a distinct setting, out-of-time-ordered correlators (OTOCs), intensely studied as a measure of information scrambling, have recently been shown to probe freeness between Heisenberg operators, the noncommutative generalization of statistical independence. Bridging these two concepts, we study the emergence of freeness in a random matrix product unitary ensemble. We prove that, with only polynomial bond dimension, these unitaries reproduce Haar values of higher-order OTOCs for local, finite-trace observables, while traceless observables instead require exponential resources. Indeed, local observables are precisely those predicted to thermalize in chaotic many-body systems according to the eigenstate thermalization hypothesis. Moreover, adding to previous literature, we show how random matrix product unitaries constitute approximate designs: we exactly compute the frame potential of the ensemble, showing convergence to the Haar value with polynomial deviations and so indicating that global observables are freely independent on-average. Our results highlight the need to refine previous notions of unitary design in the context of operator dynamics, guiding us towards protocols for quantum advantage and shedding light on the emergent complexity of chaotic many-body systems.

Dimension reduction with structure-aware quantum circuits for hybrid machine learning

Authors: Ammar Daskin

arXiv ID: 2508.00048 | Date: 2025-07-31

Abstract: Schmidt decomposition of a vector can be understood as writing the singular value decomposition (SVD) in vector form. A vector can be written as a linear combination of tensor product of two dimensional vectors by recursively applying Schmidt decompositions via SVD to all subsystems. Given a vector expressed as a linear combination of tensor products, using only the kk principal terms yields a kk-rank approximation of the vector. Therefore, writing a vector in this reduced form allows to retain most important parts of the vector while removing small noises from it, analogous to SVD-based denoising. In this paper, we show that quantum circuits designed based on a value kk (determined from the tensor network decomposition of the mean vector of the training sample) can approximate the reduced-form representations of entire datasets. We then employ this circuit ansatz with a classical neural network head to construct a hybrid machine learning model. Since the output of the quantum circuit for an 2n2^n dimensional vector is an nn dimensional probability vector, this provides an exponential compression of the input and potentially can reduce the number of learnable parameters for training large-scale models. We use datasets provided in the Python scikit-learn module for the experiments. The results confirm the quantum circuit is able to compress data successfully to provide effective kk-rank approximations to the classical processing component.

Transfer entropy and O-information to detect grokking in tensor network multi-class classification problems

Authors: Domenico Pomarico, Roberto Cilli, Alfonso Monaco, Loredana Bellantuono, Marianna La Rocca, Tommaso Maggipinto, Giuseppe Magnifico, Marlis Ontivero Ortega, Ester Pantaleo, Sabina Tangaro, Sebastiano Stramaglia, Roberto Bellotti, Nicola Amoroso

arXiv ID: 2507.23346 | Date: 2025-07-31

Abstract: Quantum-enhanced machine learning, encompassing both quantum algorithms and quantum-inspired classical methods such as tensor networks, offers promising tools for extracting structure from complex, high-dimensional data. In this work, we study the training dynamics of Matrix Product State (MPS) classifiers applied to three-class problems, using both fashion MNIST and hyper-spectral satellite imagery as representative datasets. We investigate the phenomenon of grokking, where generalization emerges suddenly after memorization, by tracking entanglement entropy, local magnetization, and model performance across training sweeps. Additionally, we employ information theory tools to gain deeper insights: transfer entropy is used to reveal causal dependencies between label-specific quantum masks, while O-information captures the shift from synergistic to redundant correlations among class outputs. Our results show that grokking in the fashion MNIST task coincides with a sharp entanglement transition and a peak in redundant information, whereas the overfitted hyper-spectral model retains synergistic, disordered behavior. These findings highlight the relevance of high-order information dynamics in quantum-inspired learning and emphasize the distinct learning behaviors that emerge in multi-class classification, offering a principled framework to interpret generalization in quantum machine learning architectures.

AC/DC spin current in ferromagnet/superconductor/normal metal trilayer systems

Authors: Koki Mizuno, Hirone Ishida, Manato Teranishi

arXiv ID: 2507.23262 | Date: 2025-07-31

Abstract: Spin pumping with superconductors has been extensively studied, particularly in double-layer systems. In this study, we investigate spin pumping in a trilayer system comprising a ferromagnetic insulator (FMI), a superconductor (SC), and a normal metal (NM). We derive the AC and DC spin currents in the NM layer induced by spin motion in the FMI under circularly polarized microwave irradiation. If we treat the spin motion as classical, the AC spin current is expressed. On the other hand, if we treat the spin motion as quantum quasiparticles, the DC spin current is derived. After these derivations, while the computational cost of evaluating the spin current is extremely high, we mitigate this using the Quantics Tensor Cross Interpolation (QTCI) method. We present numerical results showing the dependence of the spin current on temperature, microwave frequency, and superconductor layer thickness. Notably, the temperature dependence of AC and DC spin currents exhibits a coherence peak. Furthermore, we have discovered a transition structure in the dependence of the spin current on the thickness of the superconductor layer, where the dependence changes after a particular frequency.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders

Authors: Bader Aldossari, Sergey Blinov, Zhu-Xi Luo

arXiv ID: 2507.22989 | Date: 2025-07-30

Abstract: Tensor networks are an efficient platform to represent interesting quantum states of matter as well as to compute physical observables and information-theoretic quantities. We present a general protocol to construct fixed-point tensor network representations for intrinsically mixed-state topological phases, which exhibit nontrivial topological phenomena and do not have pure-state counterparts. The method exploits the power of anyon condensation in Choi states and is applicable to the cases where the target states arise from pure-state topological phases subject to strong decoherence/disorders in the Abelian sectors. Representative examples include ma^ebmâ e^b decoherence of ZN\mathbb{Z}_N toric code, decohered non-Abelian S3S_3 quantum double as well as pure ZZ/XX decoherence of arbitrary CSS codes. An example of chiral topological phases which cannot arise from local commuting projector models are also presented.

Field digitization scaling in a ZNU(1)\mathbb{Z}_N \subset U(1) symmetric model

Authors: Gabriele Calliari, Robert Ott, Hannes Pichler, Torsten V. Zache

arXiv ID: 2507.22984 | Date: 2025-07-30

Abstract: The simulation of quantum field theories, both classical and quantum, requires regularization of infinitely many degrees of freedom. However, in the context of field digitization (FD) -- a truncation of the local fields to NN discrete values -- a comprehensive framework to obtain continuum results is currently missing. Here, we propose to analyze FD by interpreting the parameter NN as a coupling in the renormalization group (RG) sense. As a first example, we investigate the two-dimensional classical NN-state clock model as a ZN\mathbb{Z}_N FD of the U(1)U(1)-symmetric XYXY-model. Using effective field theory, we employ the RG to derive generalized scaling hypotheses involving the FD parameter NN, which allows us to relate data obtained for different NN-regularized models in a procedure that we term field digitization scaling\textit{field digitization scaling} (FDS). Using numerical tensor-network calculations at finite bond dimension χχ, we further uncover an unconventional universal crossover around a low-temperature phase transition induced by finite NN, demonstrating that FDS can be extended to describe the interplay of χχ and NN. Finally, we analytically prove that our calculations for the 2D classical-statistical ZN\mathbb{Z}_N clock model are directly related to the quantum physics in the ground state of a (2+1)D ZN\mathbb{Z}_N lattice gauge theory which serves as a FD of compact quantum electrodynamics. Our study thus paves the way for applications of FDS to quantum simulations of more complex models in higher spatial dimensions, where it could serve as a tool to analyze the continuum limit of digitized quantum field theories.

Matrix product states as thin torus limits of conformal correlators

Authors: Adrián Franco-Rubio, J. Ignacio Cirac, Germán Sierra

arXiv ID: 2507.22735 | Date: 2025-07-30

Abstract: We introduce one-parameter families of spin chain ansatz wavefunctions constructed from chiral conformal field theory correlators on a torus, with the modular parameter ττ serving as the deformation parameter. In the cylinder limit ττ\to\infty, these wavefunctions reduce to infinite dimensional matrix product states. In contrast, in the thin torus limit τ0τ\to0, they become finite bond dimension matrix product states (MPS). Focusing on families derived from the SU(2)1_1 and SU(2)2_2 Wess-Zumino-Witten models, we show that in the thin torus limit they reproduce known MPS ground states, such as those of the Majumdar-Ghosh and AKLT spin chains.

Minimizing entanglement entropy for enhanced quantum state preparation

Authors: Oskari Kerppo, William Steadman, Ossi Niemimäki, Valtteri Lahtinen

arXiv ID: 2507.22562 | Date: 2025-07-30

Abstract: Quantum state preparation is an important subroutine in many quantum algorithms. The goal is to encode classical information directly to the quantum state so that it is possible to leverage quantum algorithms for data processing. However, quantum state preparation of arbitrary states scales exponentially in the number of two-qubit gates, and this makes quantum state preparation a very difficult task on quantum computers, especially on near-term noisy devices. This represents a major challenge in achieving quantum advantage. We present and analyze a novel two-step state preparation method where we first minimize the entanglement entropy of the target quantum state, thus transforming the state to one that is easier to prepare. The state with reduced entanglement entropy is then represented as a matrix product state, resulting in a high accuracy preparation of the target state. Our method is suitable for NISQ devices and we give rigorous lower bounds on the accuracy of the prepared state in terms of the entanglement entropy and demonstrate cutting-edge performance across a collection of benchmark states.

Two-Dimensional Bialgebras and Quantum Groups: Algebraic Structures and Tensor Network Realizations

Authors: José Garre-Rubio, András Molnár, Germán Sierra

arXiv ID: 2507.22541 | Date: 2025-07-30

Abstract: We introduce a framework to define coalgebra and bialgebra structures on two-dimensional (2D) square lattices, extending the algebraic theory of Hopf algebras and quantum groups beyond the one-dimensional (1D) setting. Our construction is based on defining 2D coproducts through horizontal and vertical maps that satisfy compatibility and associativity conditions, enabling the consistent growth of vector spaces over lattice sites. We present several examples of 2D bialgebras, including group-like and Lie algebra-inspired constructions and a quasi-1D coproduct instance that is applicable to Taft-Hopf algebras and to quantum groups. The approach is further applied to the quantum group Uq[su(2)]U_q[su(2)], for which we construct 2D generalizations of its generators, analyze qq-deformed singlet states, and derive a 2D R-matrix satisfying an intertwining relation in the semiclassical limit. Additionally, we show how tensor network states, particularly PEPS, naturally induce 2D coalgebra structures when supplemented with appropriate boundary conditions. Our results establish a local and algebraically consistent method to embed quantum group symmetries into higher-dimensional lattice systems, potentially connecting to the emerging theory of fusion 2-categories and categorical symmetries in quantum many-body physics.

Sequential Circuit as Generalized Symmetry on Lattice

Authors: Nathanan Tantivasadakarn, Xinyu Liu, Xie Chen

arXiv ID: 2507.22394 | Date: 2025-07-30

Abstract: Generalized symmetry extends the usual notion of symmetry to ones that are of higher-form, acting on subsystems, non-invertible, etc. The concept was originally defined in the field theory context using the idea of topological defects. On the lattice, an immediate consequence is that a symmetry twist is moved across the system by a sequential quantum circuit. In this paper, we ask how to obtain the full, potentially non-invertible symmetry action from the unitary sequential circuit and how the connection to sequential circuit constrains the properties of the generalized symmetries. We find that for symmetries that contain the trivial symmetry operator as a fusion outcome, which we call annihilable symmetries, the sequential circuit fully determines the symmetry action and puts various constraints on their fusion. In contrast, for unannihilable symmetries, like that whose corresponding twist is the Cheshire string, a further 1D sequential circuit is needed for the full description. Matrix product operator and tensor network operator representations play an important role in our discussion.

What is the topological dual of the XXZ spin Chain?

Authors: Yicheng Tang, Pradip Kattel, Natan Andrei

arXiv ID: 2507.22119 | Date: 2025-07-29

Abstract: We construct a dual symmetry-protected topological (SPT) Hamiltonian for the U(1)U(1) symmetric anisotropic spin-12\frac{1}{2} Heisenberg chain-a model that has traditionally been used to study spontaneous symmetry breaking (SSB) in both ferromagnetic and antiferromagnetic phases, with an intervening extended Luttinger liquid phase. By performing a non-local unitary transformation, we explicitly construct a local fermionic Hamiltonian that exhibits two nontrivial topological phases separated by an extended Luttinger liquid regime. We demonstrate the topological nature of these phases by analyzing the entanglement structure, deriving a non-local string order parameter, and constructing an exact zero mode operator that connects states in different fermionic parity sectors.

Phases of Interacting Fibonacci Anyons on a Ladder at Half-Filling

Authors: Nico Kirchner, Roderich Moessner, Frank Pollmann, Adam Gammon-Smith

arXiv ID: 2507.22115 | Date: 2025-07-29

Abstract: Two-dimensional many-body quantum systems can exhibit topological order and support collective excitations with anyonic statistics different from the usual fermionic or bosonic ones. With the emergence of these exotic point-like particles, it is natural to ask what phases can arise in interacting many-anyon systems. To study this topic, we consider the particular case of Fibonacci anyons subject to an anyonic tight-binding model with nearest-neighbor repulsion on a two-leg ladder. Focusing on the case of half-filling, for low interaction strengths an ''anyonic'' metal is found, whereas for strong repulsion, the anyons form an insulating charge-density wave. Within the latter regime, we introduce an effective one-dimensional model up to sixth order in perturbation theory arising from anyonic superexchange processes. We numerically identify four distinct phases of the effective model, which we characterize using matrix product state methods. These include both the ferro- and antiferromagnetic golden chain, a Z2\mathbb{Z}_2 phase, and an incommensurate phase.

Supervised Quantum Image Processing

Authors: Marco Parigi, Mehran Khosrojerdi, Filippo Caruso, Leonardo Banchi

arXiv ID: 2507.22039 | Date: 2025-07-29

Abstract: In the era of big data and artificial intelligence, the increasing volume of data and the demand to solve more and more complex computational challenges are two driving forces for improving the efficiency of data storage, processing and analysis. Quantum image processing (QIP) is an interdisciplinary field between quantum information science and image processing, which has the potential to alleviate some of these challenges by leveraging the power of quantum computing. In this work, we compare and examine the compression properties of four different Quantum Image Representations (QImRs): namely, Tensor Network Representation (TNR), Flexible Representation of Quantum Image (FRQI), Novel Enhanced Quantum Representation NEQR, and Quantum Probability Image Encoding (QPIE). Our simulations show that FRQI performs a higher compression of image information than TNR, NEQR, and QPIE. Furthermore, we investigate the trade-off between accuracy and memory in binary classification problems, evaluating the performance of quantum kernels based on QImRs compared to the classical linear kernel. Our results indicate that quantum kernels provide comparable classification average accuracy but require exponentially fewer resources for image storage.

Quantum generative modeling for financial time series with temporal correlations

Authors: David Dechant, Eliot Schwander, Lucas van Drooge, Charles Moussa, Diego Garlaschelli, Vedran Dunjko, Jordi Tura

arXiv ID: 2507.22035 | Date: 2025-07-29

Abstract: Quantum generative adversarial networks (QGANs) have been investigated as a method for generating synthetic data with the goal of augmenting training data sets for neural networks. This is especially relevant for financial time series, since we only ever observe one realization of the process, namely the historical evolution of the market, which is further limited by data availability and the age of the market. However, for classical generative adversarial networks it has been shown that generated data may (often) not exhibit desired properties (also called stylized facts), such as matching a certain distribution or showing specific temporal correlations. Here, we investigate whether quantum correlations in quantum inspired models of QGANs can help in the generation of financial time series. We train QGANs, composed of a quantum generator and a classical discriminator, and investigate two approaches for simulating the quantum generator: a full simulation of the quantum circuits, and an approximate simulation using tensor network methods. We tested how the choice of hyperparameters, such as the circuit depth and bond dimensions, influenced the quality of the generated time series. The QGAN that we trained generate synthetic financial time series that not only match the target distribution but also exhibit the desired temporal correlations, with the quality of each property depending on the hyperparameters and simulation method.

Triad representation for the anisotropic tensor renormalization group in four dimensions

Authors: Yuto Sugimoto, Shoichi Sasaki

arXiv ID: 2507.21909 | Date: 2025-07-29

Abstract: The development of tensor renormalization group (TRG) algorithm in higher dimensions is an important and urgent task, as the TRG is expected to provide a way to overcome the sign problem in lattice quantum chromodynamics (QCD) calculations at finite density. One possible approach that enables faster computations in four-dimensional lattice theories is the anisotropic tensor renormalization group (ATRG). However, the computational cost remains substantial and requires significant computational resources. In this paper, we propose a novel algorithm, called the triad-ATRG, which is based on the ATRG and other improved TRG variants with triad network representation. This method achieves lower scaling with respect to the bond dimension, while minimizing the loss of accuracy in the free energy and other physical quantities. We also present parallel implementations of both the ATRG and triad-ATRG on multiple GPUs, which significantly improve performance compared to CPU-based calculations for the four-dimensional system.

Static and Dynamical Characterization of Ground State Phases Induced by Frustration and Magnetic Field in the Spin-1 Orthogonal Dimer Chain

Authors: Ernest Ong, Dhiman Bhowmick, Sharoz Schezwen, Pinaki Sengupta

arXiv ID: 2507.21771 | Date: 2025-07-29

Abstract: The spin-11 orthogonal dimer chain is investigated using the Density Matrix Renormalization Group (DMRG) algorithm. A transformation to a basis that uses the local eigenstates of the orthogonal dimers, while retaining the local spin states for the parallel spins, allows for more effective implementation of the symmetries, as well as mitigating the entanglement bias of DMRG. A rich ground state phase diagram is obtained in the parameter space spanned by the ratio of inter- to intra-dimer interaction (which measures the degree of frustration) and an external magnetic field. Some ground state phases exhibit effective Haldane chain character, whereas others exhibit fragmentation of the ground state wavefunction, or clustering. The phases are characterized by their static properties, including (local) spin quantum number, entanglement entropy, and the spin-spin correlation function. Detailed characterization of a carefully selected set of representative states is presented. The static properties are complemented by exploring the low-energy dynamics through the calculation of the dynamic structure factor. The results provide crucial insight into the emergence of complex ground state phases from the interplay between strong interactions, geometric frustration, and external magnetic field for interacting S=1 Heisenberg spins.

Riemannian Optimization on Tree Tensor Networks with Application in Machine Learning

Authors: Marius Willner, Marco Trenti, Dirk Lebiedz

arXiv ID: 2507.21726 | Date: 2025-07-29

Abstract: Tree tensor networks (TTNs) are widely used in low-rank approximation and quantum many-body simulation. In this work, we present a formal analysis of the differential geometry underlying TTNs. Building on this foundation, we develop efficient first- and second-order optimization algorithms that exploit the intrinsic quotient structure of TTNs. Additionally, we devise a backpropagation algorithm for training TTNs in a kernel learning setting. We validate our methods through numerical experiments on a representative machine learning task.

Prime Factorization Equation from a Tensor Network Perspective

Authors: Alejandro Mata Ali, Jorge Martínez Martín, Sergio Muñiz Subiñas, Miguel Franco Hernando, Javier Sedano, Ángel Miguel García-Vico

arXiv ID: 2508.00907 | Date: 2025-07-29

Abstract: This paper presents an exact and explicit equation for prime factorization, along with an algorithm for its computation. The proposed method is based on the MeLoCoToN approach, which addresses combinatorial optimization problems through classical tensor networks. The presented tensor network performs the multiplication of every pair of possible input numbers and selects those whose product is the number to be factorized. Additionally, in order to make the algorithm more efficient, the number and dimension of the tensors and their contraction scheme are optimized. Finally, a series of tests on the algorithm are conducted, contracting the tensor network both exactly and approximately using tensor train compression, and evaluating its performance.

Variational inference and density estimation with non-negative tensor train

Authors: Xun Tang, Rajat Dwaraknath, Lexing Ying

arXiv ID: 2507.21519 | Date: 2025-07-29

Abstract: This work proposes an efficient numerical approach for compressing a high-dimensional discrete distribution function into a non-negative tensor train (NTT) format. The two settings we consider are variational inference and density estimation, whereby one has access to either the unnormalized analytic formula of the distribution or the samples generated from the distribution. In particular, the compression is done through a two-stage approach. In the first stage, we use existing subroutines to encode the distribution function in a tensor train format. In the second stage, we use an NTT ansatz to fit the obtained tensor train. For the NTT fitting procedure, we use a log barrier term to ensure the positivity of each tensor component, and then utilize a second-order alternating minimization scheme to accelerate convergence. In practice, we observe that the proposed NTT fitting procedure exhibits drastically faster convergence than an alternative multiplicative update method that has been previously proposed. Through challenging numerical experiments, we show that our approach can accurately compress target distribution functions.

Embedding-Aware Quantum-Classical SVMs for Scalable Quantum Machine Learning

Authors: Sebastián Andrés Cajas Ordóñez, Luis Fernando Torres Torres, Mario Bifulco, Carlos Andrés Durán, Cristian Bosch, Ricardo Simón Carbajo

arXiv ID: 2508.00024 | Date: 2025-07-28

Abstract: Quantum Support Vector Machines face scalability challenges due to high-dimensional quantum states and hardware limitations. We propose an embedding-aware quantum-classical pipeline combining class-balanced k-means distillation with pretrained Vision Transformer embeddings. Our key finding: ViT embeddings uniquely enable quantum advantage, achieving up to 8.02% accuracy improvements over classical SVMs on Fashion-MNIST and 4.42% on MNIST, while CNN features show performance degradation. Using 16-qubit tensor network simulation via cuTensorNet, we provide the first systematic evidence that quantum kernel advantage depends critically on embedding choice, revealing fundamental synergy between transformer attention and quantum feature spaces. This provides a practical pathway for scalable quantum machine learning that leverages modern neural architectures.

The Augmented Tree Tensor Network Cookbook

Authors: Nora Reinić, Luka Pavešić, Daniel Jaschke, Simone Montangero

arXiv ID: 2507.21236 | Date: 2025-07-28

Abstract: An augmented tree tensor network (aTTN) is a tensor network ansatz constructed by applying a layer of unitary disentanglers to a tree tensor network. The disentanglers absorb a part of the system's entanglement. This makes aTTNs suitable for simulating higher-dimensional lattices, where the entanglement increases with the lattice size even for states that obey the area law. These lecture notes serve as a detailed guide for implementing the aTTN algorithms. We present a variational algorithm for ground state search and discuss the measurement of observables, and offer an open-source implementation within the Quantum TEA library. We benchmark the performance of the ground state search for different parameters and hyperparameters in the square lattice quantum Ising model and the triangular lattice Heisenberg model for up to 32×3232 \times 32 spins. The benchmarks identify the regimes where the aTTNs offer advantages in accuracy relative to computational cost compared to matrix product states and tree tensor networks.

Emergence of a Boundary-Sensitive Phase in Hyperbolic Ising Models

Authors: Xingzhi Wang, Zohar Nussinov, Gerardo Ortiz

arXiv ID: 2507.21044 | Date: 2025-07-28

Abstract: Physical systems defined on hyperbolic lattices may exhibit phases of matter that only emerge due to negative curvature. We focus on the case of the Ising model under open boundary conditions and show that an ``intermediate'' phase emerges in addition to standard (high-temperature) paramagnetic and (low-temperature) ferromagnetic phases. When performing the Kramers-Wannier duality the fact that it alters boundary conditions becomes crucial, since a finite fraction of lattice sites lie on the boundary. We propose to characterize this ``intermediate'' phase by its sensitivity to boundary conditions, wherein bulk ordering is not spontaneous but rather induced by boundary effects, setting it apart from the Landau paradigm of spontaneous symmetry breaking. By developing a Z2\mathbb{Z}_2 symmetry restricted extension of the Corner Transfer Matrix Renormalization Group method, we provide numerical evidence for the existence of all three distinct phases and their corresponding two-stage phase transitions, thereby establishing the complete phase diagram. We also establish how the (spontaneous) intermediate-to-ferromagnetic and the (induced) paramagnetic-to-intermediate transition points are related by the Kramers-Wannier duality relation. We discuss a holographic correspondence between boundary and bulk behaviors and derive exact expressions for boundary correlation functions on Cayley trees.

Optimizing adsorption configurations on alloy surfaces using Tensor Train Optimizer

Authors: Tuan Minh Do, Tomoya Shiota, Wataru Mizukami

arXiv ID: 2507.20827 | Date: 2025-07-28

Abstract: Understanding how molecules arrange on surfaces is fundamental to surface chemistry and essential for the rational design of catalytic and functional materials. In particular, the energetically most stable configuration provides valuable insight into adsorption-related processes. However, the search for this configuration is a global optimization problem with exponentially growing complexity as the number of adsorbates and possible adsorption sites increases. To address this, we express the adsorption energy as a sum of multi-adsorbate interaction terms, evaluated using our in-house trained machine learning interatomic potential MACE-Osaka24, and formulate the search for the most stable configuration as a higher-order unconstrained binary optimization (HUBO) problem. We employ a tensor-train-based method, Tensor Train Optimizer (TTOpt), to solve the HUBO problem and identify optimal adsorption configurations of CO and NO molecules on various alloys up to full surface coverage. Our results show that including interaction terms up to third order may be sufficient to approximate adsorption energies within chemical accuracy and to identify optimal configurations. We also observed that TTOpt performs better with the HUBO formulation, suggesting that third-order terms help preserve correlations between adsorption sites, which allow TTOpt to optimize configurations more effectively. The extensive benchmarks across various alloys, surface geometries, and adsorbates demonstrate the robustness and applicability of using TTOpt to solve HUBO-type global optimization problems in surface chemistry. In contrast to quantum and digital annealers, which have recently been applied to similar global optimization tasks but are restricted to cost functions with at most quadratic terms, our approach can incorporate higher-order terms in a straightforward manner and does not require specialized hardware.

Optimizing Tensor Network Partitioning using Simulated Annealing

Authors: Manuel Geiger, Qunsheng Huang, Christian B. Mendl

arXiv ID: 2507.20667 | Date: 2025-07-28

Abstract: Tensor networks have proven to be a valuable tool, for instance, in the classical simulation of (strongly correlated) quantum systems. As the size of the systems increases, contracting larger tensor networks becomes computationally demanding. In this work, we study distributed memory architectures intended for high-performance computing implementations to solve this task. Efficiently distributing the contraction task across multiple nodes is critical, as both computational and memory costs are highly sensitive to the chosen partitioning strategy. While prior work has employed general-purpose hypergraph partitioning algorithms, these approaches often overlook the specific structure and cost characteristics of tensor network contractions. We introduce a simulated annealing-based method that iteratively refines the partitioning to minimize the total operation count, thereby reducing time-to-solution. The algorithm is evaluated on MQT Bench circuits and achieves an 8×\times average reduction in computational cost and an 8×\times average reduction in memory cost compared to a naive partitioning.

Neural Importance Resampling: A Practical Sampling Strategy for Neural Quantum States

Authors: Eimantas Ledinauskas, Egidijus Anisimovas

arXiv ID: 2507.20510 | Date: 2025-07-28

Abstract: Neural quantum states (NQS) have emerged as powerful tools for simulating many-body quantum systems, but their practical use is often hindered by limitations of current sampling techniques. Markov chain Monte Carlo (MCMC) methods suffer from slow mixing and require manual tuning, while autoregressive NQS impose restrictive architectural constraints that complicate the enforcement of symmetries and the construction of determinant-based multi-state wave functions. In this work, we introduce Neural Importance Resampling (NIR), a new sampling algorithm that combines importance resampling with a separately trained autoregressive proposal network. This approach enables efficient and unbiased sampling without constraining the NQS architecture. We demonstrate that NIR supports stable and scalable training, including for multi-state NQS, and mitigates issues faced by MCMC and autoregressive approaches. Numerical experiments on the 2D transverse-field Ising and J1J_1-J2J_2 Heisenberg models show that NIR outperforms MCMC in challenging regimes and yields results competitive with state of the art methods. Our results establish NIR as a robust alternative for sampling in variational NQS algorithms.

Steady state representations for the harmonic process

Authors: Rouven Frassek

arXiv ID: 2507.20436 | Date: 2025-07-27

Abstract: In this note we discuss how the matrix product solution for the steady state of the harmonic process is obtained from the solutions already known in the literature, i.e. the closed-form expression derived in arXiv:2107.01720 and the nested integral form obtained in arXiv:2307.02793 and arXiv:2307.14975. Our results clarify the relation between the three representations of the steady state and provide the matrix product solution that has not been available for this model before.

Entanglement Halos

Authors: Nadir Samos Sáenz de Buruaga, Silvia N. Santalla, Germán Sierra, Javier Rodríguez-Laguna

arXiv ID: 2507.20430 | Date: 2025-07-27

Abstract: We introduce the concept of entanglement halos, a set of strongly entangled distant sites within the ground state of a quantum many-body system. Such halos emerge in star-like systems with exponentially decaying couplings, as we show using both free-fermions and the spin-1/2 antiferromagnetic Heisenberg model. Depending on the central connectivity, entanglement halos may exhibit trivial and non trivial symmetry-protected topological features. Our findings highlight how geometry and connectivity can generate complex entanglement structures with rich physical content, which can be experimentally accessible via state-of-the-art technologies.

Biorthogonal quench dynamics of entanglement and quantum geometry in PT-symmetric non-Hermitian systems

Authors: Hsueh-Hao Lu, Po-Yao Chang

arXiv ID: 2507.20155 | Date: 2025-07-27

Abstract: We explore the quench dynamics of PT-symmetric non-Hermitian systems by utilizing the biorthogonal formalism. We analyze quench dynamics of observable quantities, the quantum geometric tensor, and various entanglement quantities, including the entanglement entropy, the SVD entropy, and the Tu-Tzeng-Chang entropy. Our results show that a sudden quench into a PT-broken phase generally leads to exponential growth in these quantities, driven by the biorthogonal density matrix's non-positivity. In contrast to generic interacting systems, we observe a surprising linear decay in the TTC entropy for non-interacting fermionic systems. This finding originates from the approximate spectral symmetry of the biorthogonal reduced density matrix, and we confirm our findings using the Yang-Lee and non-Hermitian XXZ models.

Anyonic Josephson junctions: Dynamical and ground-state properties

Authors: Jessica John Britto

arXiv ID: 2507.20044 | Date: 2025-07-26

Abstract: Bosons with density-dependent hopping on a one dimensional lattice have been shown to emulate anyonic particles with fractional exchange statistics. Leveraging this, we construct a Josephson junction setup, where an insulating barrier in the form of a Mott-insulator is sandwiched between two superfluid phases. This is obtained by spatially varying either the statistical phase or the strength of the on-site interaction potential on which the ground state of the system depends. Utilizing numerical methods such as exact diagonalization and density renormalization group theory, the ground state properties of this setup are investigated to understand the Josephson effect in a strongly correlated regime. The dynamical properties of this model for different configurations of this model are analyzed to find the configurations that can produce the Josephson effect. Furthermore, it is observed that continuous particle flow over time is achievable in this proposed model solely by creating an initial phase difference without any external biasing.

Equivariant Parameter Families of Spin Chains: A Discrete MPS Formulation

Authors: Ken Shiozaki

arXiv ID: 2507.19932 | Date: 2025-07-26

Abstract: We analyze topological phase transitions and higher Berry curvature in one-dimensional quantum spin systems, using a framework that explicitly incorporates the symmetry group action on the parameter space. Based on a GG-compatible discretization of the parameter space, we incorporate both group cochains and parameter-space differentials, enabling the systematic construction of equivariant topological invariants. We derive a fixed-point formula for the higher Berry invariant in the case where the symmetry action has isolated fixed points. This reveals that the phase transition point between Haldane and trivial phases acts as a monopole-like defect where higher Berry curvature emanates. We further discuss hierarchical structures of topological defects in the parameter space, governed by symmetry reductions and compatibility with subgroup structures.

Local Potential Functional Embedding Theory of Molecular Systems: Localized Orbital-Based Embedding from an Exact Density-Functional Perspective

Authors: W. Makhlouf, B. Senjean, E. Fromager

arXiv ID: 2507.19591 | Date: 2025-07-25

Abstract: Localized orbital-based quantum embedding, as originally formulated in the context of density matrix embedding theory (DMET), is revisited from the perspective of lattice density functional theory (DFT). An in-principle exact (in the sense of full configuration interaction) formulation of the theory, where the occupations of the localized orbitals play the role of the density, is derived for any (model or ab initio) electronic Hamiltonian. From this general formalism we deduce an exact relation between the local Hartree-exchange-correlation (Hxc) potential of the full-size Kohn-Sham (KS) lattice-like system and the embedding chemical potential that is adjusted on each embedded fragment, individually, such that both KS and embedding cluster systems reproduce the exact same local density. When well-identified density-functional approximations (that find their justification in the strongly correlated regime) are applied, a practical self-consistent local potential functional embedding theory (LPFET), where the local Hxc potential becomes the basic variable, naturally emerges from the theory. LPFET differs from previous density embedding approaches by its fragment-dependent embedding chemical potential expression, which is a simple functional of the Hxc potential. Numerical calculations on prototypical systems show the ability of such an ansatz to improve substantially the description of density profiles (localized orbitals occupation numbers in this context) in strongly correlated systems.

From weakly interacting spinons to tightly bound triplons in the frustrated quantum spin-Peierls chain

Authors: Pyeongjae Park, Bo Xiao, Karolina Górnicka, Andrew F. May, Jiaqiang Yan, Ryoichi Kajimoto, Mitsutaka Nakamura, Matthew B. Stone, Gábor B. Halász, Andrew D. Christianson

arXiv ID: 2507.19412 | Date: 2025-07-25

Abstract: Fractionalized quasiparticles and their confinement into emergent bound states lie at the heart of modern quantum magnetism. While the evolution into magnonic bound states has been well characterized, experimental insight into the analogous transition to triplons remains limited. Here, using high-resolution neutron spectroscopy and state-of-the-art spin dynamics simulations, we uncover the transformation from weakly interacting spinons to tightly bound triplons in the spin-Peierls compound CuGeO3. Quantitative comparisons between the measured spectra and tensor network simulations reveal substantial next-nearest-neighbor frustration and weak external dimerization, placing the system deep within the spontaneously dimerized regime and near the exactly solvable Majumdar-Ghosh point. We further show an energy- and temperature-dependent evolution between two contrasting quasiparticle regimes: deconfined spinons with markedly suppressed interactions by frustration, and coherent triplonic bound states with no observable spinon degrees of freedom. Remarkably, triplon character persists into the two-particle regime, forming a structured two-triplon continuum with a spectral feature associated with a van Hove singularity at its lower boundary. These findings challenge the conventional view that robust triplons require strong external dimerization and demonstrate how the interplay between frustration and dimerization can reshape fractionalization and confinement.

Tensor Networks for Liquids in Heterogeneous Systems

Authors: Zachary A. Johnson, Luciano G. Silvestri, Pierson Guthrey, Michael S. Murillo

arXiv ID: 2507.19352 | Date: 2025-07-25

Abstract: Many-body correlations in strongly coupled liquids and plasmas are critical for many applications in nanofluids, biology, and fusion-related plasma physics, but their description in fully heterogeneous environments remains challenging due to the high-dimensional equations involved. Recently, tensor network decompositions have emerged as powerful tools for tackling such equations by reducing memory usage and computational complexity. In this paper, we solve for equilibrium density and density-density correlation functions of liquids in confined heterogeneous environments using tensor network methods. We demonstrate that these functions admit high compression when their lengthscale dependence is encoded via quantized tensor trains or when their spatial-coordinate dependence is represented in standard tensor-train format, but not with respect to their dependence on distinct particle coordinates.

Hybrid tensor network and neural network quantum states for quantum chemistry

Authors: Zibo Wu, Bohan Zhang, Wei-Hai Fang, Zhendong Li

arXiv ID: 2507.19276 | Date: 2025-07-25

Abstract: Neural network quantum states (NQS) have emerged as a powerful and flexible framework for addressing quantum many-body problems. While successful for model Hamiltonians, their application to molecular systems remains challenging for several reasons. In this work, we introduce three innovations to overcome some of the key limitations. (1) We propose two novel ansätzet hat hybridize tensor network and neural network states for addressing initialization challenges and enhancing the expressivity of tensor networks. First, we develop a bounded-degree graph recurrent neural network (BDG-RNN) ansatz that leverages graph-based updates, enabling applications to molecular electronic structure problems. Second, we introduce restricted Boltzmann machine (RBM) inspired correlators to further enhance expressivity and improve accuracy, without dramatically modifying the underlying variational Monte Carlo (VMC) optimization framework. (2) We introduce a semi-stochastic algorithm for local energy evaluation, which significantly reduces computational cost while maintaining high accuracy. Combining these advances, we demonstrate that our approaches can achieve chemical accuracy in challenging systems, including the one-dimensional hydrogen chain H50, the iron-sulfur cluster [Fe2S2(SCH3)4]^{2-}, and a three-dimensional 3×3×23 \times 3 \times 2 hydrogen cluster H18. These methods are implemented in an open-source package - PyNQS (https://github.com/Quantum-Chemistry-Group-BNU/PyNQS) to advance NQS methodologies for quantum chemistry.

Barren-plateau free variational quantum simulation of Z2 lattice gauge theories

Authors: Fariha Azad, Matteo Inajetovic, Stefan Kühn, Anna Pappa

arXiv ID: 2507.19203 | Date: 2025-07-25

Abstract: In this work, we design a variational quantum eigensolver (VQE) suitable for investigating ground states and static string breaking in a Z2\mathbb{Z}_2 lattice gauge theory (LGT). We consider a two-leg ladder lattice coupled to Kogut-Susskind staggered fermions and verify the results of the VQE simulations using tensor network methods. We find that for varying Hamiltonian parameter regimes and in the presence of external charges, the VQE is able to arrive at the gauge-invariant ground state without explicitly enforcing gauge invariance through penalty terms. Additionally, experiments showing string breaking are performed on IBM's quantum platform. Thus, VQEs are seen to be a promising tool for Z2\mathbb{Z}_2 LGTs, and could pave the way for studies of other gauge groups. We find that the scaling of gradients with the number of qubits is favorable for avoiding barren plateaus. At the same time, it is not clear how to efficiently simulate the LGT using classical methods. Furthermore, strategies that avoid barren plateaus arise naturally as features of LGTs, such as choosing the initialization by setting the Gauss law sector and restricting the Hilbert space to the gauge-invariant subspace.

Entanglement across scales: Quantics tensor trains as a natural framework for renormalization

Authors: Stefan Rohshap, Jheng-Wei Li, Alena Lorenz, Serap Hasil, Karsten Held, Anna Kauch, Markus Wallerberger

arXiv ID: 2507.19069 | Date: 2025-07-25

Abstract: Understanding entanglement remains one of the most intriguing problems in physics. While particle and site entanglement have been studied extensively, the investigation of length or energy scale entanglement, quantifying the information exchange between different length scales, has received far less attention. Here, we identify the quantics tensor train (QTT) technique, a matrix product state-inspired approach for overcoming computational bottlenecks in resource-intensive numerical calculations, as a renormalization group method by analytically expressing an exact cyclic reduction-based real-space renormalization scheme in QTT language, which serves as a natural formalism for the method. In doing so, we precisely match the QTT bond dimension, a measure of length scale entanglement, to the number of rescaled couplings generated in each coarse-graining renormalization step. While QTTs have so far been applied almost exclusively to numerical problems in physics, our analytical calculations demonstrate that they are also powerful tools for mitigating computational costs in semi-analytical treatments. We present our results for the one-dimensional tight-binding model with n-th-nearest-neighbor hopping, where the 2n rescaled couplings generated in the renormalization procedure precisely match the QTT bond dimension of the one-particle Green's function.

Surface growth scheme for bulk reconstruction and TTˉT\bar T deformation

Authors: Hao-Chun Liang, Jia-Rui Sun, Yuan Sun

arXiv ID: 2507.18435 | Date: 2025-07-24

Abstract: In this paper, we study the dynamical connection between the surface growth scheme and the conformal field theory with TTˉT\bar{T} deformation. By utilizing the extended one-shot entanglement distillation tensor network, we find that the iterative growth, i.e. radial evolution of homogenous and isotropic bulk minimal surfaces in asymptotically anti-de Sitter (AdS) spacetime can be mapped to the TTˉT\bar{T} operator flow driven by the deformation parameter. Our results show that the TTˉT\bar{T} deformation can provide a dynamical mechanism for the surface growth in asymptotically AdS spacetime, which may shed light on reconstructing bulk gravitational dynamics from the surface growth scheme.

Parameter-Efficient Fine-Tuning of 3D DDPM for MRI Image Generation Using Tensor Networks

Authors: Binghua Li, Ziqing Chang, Tong Liang, Chao Li, Toshihisa Tanaka, Shigeki Aoki, Qibin Zhao, Zhe Sun

arXiv ID: 2507.18112 | Date: 2025-07-24

Abstract: We address the challenge of parameter-efficient fine-tuning (PEFT) for three-dimensional (3D) U-Net-based denoising diffusion probabilistic models (DDPMs) in magnetic resonance imaging (MRI) image generation. Despite its practical significance, research on parameter-efficient representations of 3D convolution operations remains limited. To bridge this gap, we propose Tensor Volumetric Operator (TenVOO), a novel PEFT method specifically designed for fine-tuning DDPMs with 3D convolutional backbones. Leveraging tensor network modeling, TenVOO represents 3D convolution kernels with lower-dimensional tensors, effectively capturing complex spatial dependencies during fine-tuning with few parameters. We evaluate TenVOO on three downstream brain MRI datasets-ADNI, PPMI, and BraTS2021-by fine-tuning a DDPM pretrained on 59,830 T1-weighted brain MRI scans from the UK Biobank. Our results demonstrate that TenVOO achieves state-of-the-art performance in multi-scale structural similarity index measure (MS-SSIM), outperforming existing approaches in capturing spatial dependencies while requiring only 0.3% of the trainable parameters of the original model. Our code is available at: https://github.com/xiaovhua/tenvoo

Resource-Efficient Simulations of Particle Scattering on a Digital Quantum Computer

Authors: Yahui Chai, Joe Gibbs, Vincent R. Pascuzzi, Zoë Holmes, Stefan Kühn, Francesco Tacchino, Ivano Tavernelli

arXiv ID: 2507.17832 | Date: 2025-07-23

Abstract: We develop and demonstrate methods for simulating the scattering of particle wave packets in the interacting Thirring model on digital quantum computers, with hardware implementations on up to 80 qubits. We identify low-entanglement time slices of the scattering dynamics and exploit their efficient representation by tensor networks. Circuit compression based on matrix product state techniques yields on average a reduction by a factor of 3.2 in circuit depth compared to conventional approaches, allowing longer evolution times to be evaluated with higher fidelity on contemporary quantum processors. Utilizing zero-noise extrapolation in combination with Pauli twirling, on quantum hardware we accurately simulate the full scattering dynamics on 40 qubits, and further demonstrate the wave packet state-preparation on 80 qubits.

Instability of explicit time integration for strongly quenched dynamics with neural quantum states

Authors: Hrvoje Vrcan, Johan H. Mentink

arXiv ID: 2507.17421 | Date: 2025-07-23

Abstract: Neural quantum states have recently demonstrated significant potential for simulating quantum dynamics beyond the capabilities of existing variational ansätze. However, studying strongly driven quantum dynamics with neural networks has proven challenging so far. Here, we focus on assessing several sources of numerical instabilities that can appear in the simulation of quantum dynamics based on the time-dependent variational principle (TDVP) with the computationally efficient explicit time integration scheme. Focusing on the restricted Boltzmann machine architecture, we compare solutions obtained by TDVP with analytical solutions and implicit methods as a function of the quench strength. Interestingly, we uncover a quenching strength that leads to a numerical breakdown in the absence of Monte Carlo noise, despite the fact that physical observables don't exhibit irregularities. This breakdown phenomenon appears consistently across several different TDVP formulations, even those that eliminate small eigenvalues of the Fisher matrix or use geometric properties to recast the equation of motion. We provide evidence that the nature of the instability stems from stiffness of the dynamics of the variational parameters, despite the absence of stiffness in the exact quantum dynamics. We conclude that alternative methods need to be developed to leverage the computational efficiency of explicit time integration of the TDVP equations for simulating strongly nonequilibrium quantum dynamics with neural-network quantum states.

Advancing Quantum State Preparation Using Decision Diagram with Local Invertible Maps

Authors: Xin Hong, Aochu Dai, Chenjian Li, Sanjiang Li, Shenggang Ying, Mingsheng Ying

arXiv ID: 2507.17170 | Date: 2025-07-23

Abstract: Quantum state preparation (QSP) is a fundamental task in quantum computing and quantum information processing. It is critical to the execution of many quantum algorithms, including those in quantum machine learning. In this paper, we propose a family of efficient QSP algorithms tailored to different numbers of available ancilla qubits - ranging from no ancilla qubits, to a single ancilla qubit, to a sufficiently large number of ancilla qubits. Our approach exploits the power of Local Invertible Map Tensor Decision Diagrams (LimTDDs) - a highly compact representation of quantum states that combines tensor networks and decision diagrams to reduce quantum circuit complexity. Extensive experiments demonstrate that our methods significantly outperform existing approaches and exhibit better scalability for large-scale quantum states, both in terms of runtime and gate complexity. Furthermore, our method shows exponential improvement in best-case scenarios.

Thermal Hall transport in Kitaev spin liquids

Authors: Tsuyoshi Okubo, Joji Nasu, Takahiro Misawa, Yukitoshi Motome

arXiv ID: 2507.16558 | Date: 2025-07-22

Abstract: We investigate the thermal Hall conductivity in the Kitaev model with additional interactions under a magnetic field, employing a finite-temperature tensor network method benchmarked by a thermal pure quantum state technique. We find that the thermal Hall conductivity divided by temperature, κxy/Tκ_{xy}/T, significantly overshoots the value of the half-integer quantization and exhibits a pronounced hump while decreasing temperature. Moreover, we show that the field-direction dependence of κxy/Tκ_{xy}/T is consistent with the sign of the Chern number associated with the Majorana fermions across a wide range of magnetic fields. We also demonstrate that the additional off-diagonal interactions, known as the ΓΓ and ΓΓ^{\prime} terms, considerably affect κxy/Tκ_{xy}/T. In particular, we show that positive ΓΓ and negative ΓΓ^{\prime} lead to a remarkable enhancement in the intermediate temperature region. From the comparison with the classical counterpart, we reveal that the effects of the ΓΓ term go beyond the classical picture, indicating significant quantum fluctuation effects, while those of the ΓΓ^\prime term are well captured at the classical level. These comprehensive analyses indicate that the enhanced thermal Hall response is consistently explained by dominant contributions from topological Majorana fermions, even within the polarized regime beyond the critical field. Our approach not only establishes a robust theoretical framework for understanding the thermal Hall transport in Kitaev materials such as αα-RuCl3_{3}, but also offers a promising pathway to bridge the gap between theories and experiments across a wide range of strongly correlated materials.

"Odd" Toric Code in a tilted field: Higgs-confinement multicriticality, spontaneous self-duality symmetry breaking, and valence bond solids

Authors: Umberto Borla, Ayush De, Snir Gazit

arXiv ID: 2507.16523 | Date: 2025-07-22

Abstract: We investigate the quantum phase diagram of an ``odd'' variant of the two-dimensional Ising Fradkin--Shenker model, characterized by a uniform background of static ee and mm charges. Using large-scale tensor network and exact diagonalization methods, we determine the topology of the phase diagram, identifying an ``odd'' deconfined phase, confinement- and Higgs-induced valence bond solids (VBS), and a trivial paramagnet. Most notably, we uncover an exotic multicritical point along the self-dual line, where electric and magnetic excitations are related by an enriched Z2\mathbb{Z}_2 duality. This transition is marked by the simultaneous onset of confinement, Higgs condensation, translational symmetry breaking, and spontaneous duality symmetry breaking. Within our numerical accuracy, the transition appears continuous, involving the softening of excitation gaps for ee and mm anyons at finite momentum. At intermediate couplings, we further identify VBS phases with enlarged unit cells, potentially indicating frustration-induced crystalline order beyond commensurate limits.

On two-dimensional tensor network group symmetries

Authors: José Garre-Rubio, András Molnár

arXiv ID: 2507.16475 | Date: 2025-07-22

Abstract: We introduce two-dimensional tensor network representations of finite groups carrying a 4-cocycle index. We characterize the associated gapped (2+1)D phases that emerge when these anomalous symmetries act on tensor network ground states. We further develop related tensor network unitaries that generate symmetric states representing (3+1)D symmetry protected topological phases. Although aspects of these constructions have been previously addressed, our contribution unifies them within a single tensor network framework and emphasizes the explicit formulation of local tensor equations encoding global consistency conditions.

Beyond fragmented dopant dynamics in quantum spin lattices: Robust localization and non-Gaussian diffusion

Authors: Mingru Yang, Sajant Anand, Kristian Knakkergaard Nielsen

arXiv ID: 2507.16042 | Date: 2025-07-21

Abstract: The motion of dopants in magnetic spin lattices has received tremendous attention for at least four decades due to its connection to high-temperature superconductivity. Despite these efforts, we lack a complete understanding of their behavior, especially out of the equilibrium and at nonzero temperatures. In this paper, we take a significant step towards a much deeper understanding based on state-of-the-art matrix-product-state calculations. In particular, we investigate the non-equilibrium dynamics of a dopant in two-leg tt--JJ ladders with antiferromagnetic XXZ spin interactions. In the Ising limit, we find that the dopant is localized for all investigated nonzero temperatures due to an emergent disordered potential, with a localization length controlled by the underlying correlation length of the spin lattice, which increases exponentially with decreasing temperature. The dopant, hereby, only delocalizes asymptotically in the zero temperature limit. This greatly generalizes the localization effect discovered recently in Hilbert space fragmented models. In the presence of spin-exchange processes at rate αα, the dopant diffuses with a diffusion coefficient, DhD_h, depending non-monotonically on αα. It initially increases linearly as DhαD_h \propto α for α1α\ll 1 before dropping off as α1α^{-1} for α>1α> 1. Moreover, we show that the underlying spin dynamics at infinite temperature behaves qualitatively the same, albeit with important quantitative differences. We substantiate these findings by showing that the dynamics features self-similar scaling behavior, which strongly deviates from the Gaussian behavior of regular diffusion, especially for weak spin exchange. Finally, we show that the diffusion coefficient DhD_h follows an Arrhenius relation at high temperatures, whereby it is exponentially suppressed upon cooling.

Impact of finite squeezing on near-term quantum computations using GKP qubits

Authors: Frederik K. Marqversen, Andreas B. Michelsen, Janus H. Wesenberg, Nikolaj T. Zinner

arXiv ID: 2507.15955 | Date: 2025-07-21

Abstract: We present the first detailed simulation of a measurement based quantum computation based on Gottesman-Kitaev-Preskill (GKP) qubits within a quad-rail lattice (QRL) cluster state involving over 100 GKP modes. This was enabled by the recently developed functional matrix product states (FMPS) framework, with which we simulate continuous-variable (CV) quantum circuits while explicitly modelling intrinsic coherent error sources due to finite squeezing. We perform simulated randomised benchmarking across squeezing levels between 5 and 15 dB and find strong agreement with analytical estimates for high quality GKP qubits. As a demonstration of practical computation, we simulate a three-qubit Grover's algorithm within the QRL and identify a fundamental squeezing threshold -- approximately 10 dB -- beyond which the algorithm outperforms classical probability bounds.

Interaction-induced nematic Dirac semimetal from quadratic band touching: A constrained-path quantum Monte Carlo study

Authors: Zi Hong Liu, Hongyu Lu, Zi Yang Meng, Lukas Janssen

arXiv ID: 2507.15668 | Date: 2025-07-21

Abstract: Electronic systems with quadratic band touchings, commonly found in two- and three-dimensional materials such as Bernal-stacked bilayer graphene, kagome metals, HgTe, and pyrochlore iridates, have attracted significant interest concerning the role of interactions in shaping their electronic properties. However, even in the simplest model of spinless fermions on a two-dimensional checkerboard lattice, the quantum phase diagram as a function of nearest-neighbor interaction remains under debate. We employ constrained-path quantum Monte Carlo simulations (CP-QMC) simulations to investigate the problem using a two-dimensional torus geometry. We cross-validate our results on small lattices by comparing them with density-matrix renormalization group calculations, finding quantitative agreement. In particular, we implement an improved optimization scheme within the CP-QMC simulations, enabling the identification of a bond-nematic Dirac semimetal phase that was found in tensor-network studies on cylindrical geometries, but remains inaccessible to Hartree-Fock mean-field methods. The CP-QMC approach makes it possible to establish the emergence of this phase in a geometry that preserves lattice rotational symmetry and permits extrapolation to the thermodynamic limit. Our results show that the quantum phase diagram of spinless fermions on the checkerboard lattice with nearest-neighbor repulsion features three interaction-induced phases at half filling: a quantum anomalous Hall insulator at weak coupling, a bond-nematic Dirac semimetal at intermediate coupling, and a site-nematic insulator at strong coupling.

One-point functions in AdS/dCFT: MPS and twisted Yangian

Authors: Xin Qian

arXiv ID: 2507.15462 | Date: 2025-07-21

Abstract: I focus on the scalar one-point functions in SO(6) sector of D5-D3 probe-brane set-up. Start with a general introduction of integrability, I explore both coordinate Bethe ansatz and algebraic Bethe ansatz, with possible generalization. I then shortly review how to use the Bethe ansatz in N=4N = 4 super Yang-Mills theory, and then apply such procedure to the D5-D3 system. The dual field theory of such system corresponds to a defected version of N=4N = 4 super Yang-Mills theory, where the one-point functions of certain scalars are non-zero. The calculation of one-point functions is mapped to the overlap between matrix product states and Bethe states. The matrix product states are found to be solutions of the twisted Boundary Yang-Baxter equation, and equivalently the representations of extended twisted Yangian. By dressing procedure or coproduct property, we can connect the scalar matrix product state and higher dimension matrix product states. We have used the branching rules to find the connection with some detailed parameters needed to be fixed. Such method can not only be used for calculations of one-point functions in probe-branes system, but also shed some light on non-equilibrium system.

Multipartite Markov Gaps and Entanglement Wedge Multiway Cuts

Authors: Norihiro Iizuka, Akihiro Miyata, Mitsuhiro Nishida

arXiv ID: 2507.15262 | Date: 2025-07-21

Abstract: The Markov gap, defined as the difference between reflected entropy and mutual information, serves as a diagnostic for quantum recoverability and multipartite entanglement. In holographic settings, it admits a geometric interpretation as the deviation between entanglement wedge cross-sections and RT surfaces. Motivated by this holographic perspective, we propose a generalization of the Markov gap to multipartite systems by using a reflected multi-entropy. The resulting Multipartite Markov gap can capture geometric obstructions to bulk reconstruction. We investigate the properties of this quantity from both information-theoretic and holographic viewpoints, and examine its potential operational significance through candidate recovery maps. We further introduce the genuine reflected multi-entropy, which is designed to vanish for states containing only lower-partite entanglement. Together, these quantities offer complementary probes of recoverability and multipartite structure in holographic quantum systems.

Planted Solutions in Quantum Chemistry: Generating Non-Trivial Hamiltonians with Known Ground States

Authors: Linjun Wang, Joshua T. Cantin, Smik Patel, Ignacio Loaiza, Rick Huang, Artur F. Izmaylov

arXiv ID: 2507.15166 | Date: 2025-07-21

Abstract: Generating large, non-trivial quantum chemistry test problems with known ground-state solutions remains a core challenge for benchmarking electronic structure methods. Inspired by planted-solution techniques from combinatorial optimization, we introduce four classes of Hamiltonians with embedded, retrievable ground states. These Hamiltonians mimic realistic electronic structure problems, support adjustable complexity, and are derived from reference systems. Crucially, their ground-state energies can be computed exactly, provided the construction parameters are known. To obscure this structure and control perceived complexity, we introduce techniques such as killer operators, balance operators, and random orbital rotations. We showcase this framework using examples based on homogeneous catalysts of industrial relevance and validate tunable difficulty through density matrix renormalization group (DMRG) convergence behavior. Beyond enabling scalable, ground-truth benchmark generation, our approach offers a controlled setting to explore the limitations of electronic structure methods and investigate how Hamiltonian structure influences ground state solution difficulty.

Spiral renormalization group flow and universal entanglement spectrum of the non-Hermitian 5-state Potts model

Authors: Vic Vander Linden, Boris De Vos, Kevin Vervoort, Frank Verstraete, Atsushi Ueda

arXiv ID: 2507.14732 | Date: 2025-07-19

Abstract: The quantum 55-state Potts model is known to possess a perturbative description using complex conformal field theory (CCFT), the analytic continuation of ``theory space" to a complex plane. To study the corresponding complex fixed point on the lattice, the model must be deformed by an additional non-Hermitian term due to its complex coefficient λλ. Although the variational principle breaks down in this case, we demonstrate that tensor network algorithms are still capable of simulating these non-Hermitian theories. We access system sizes up to L=28L = 28, which enable the observation of the theoretically predicted spiral flow of the running couplings. Moreover, we reconstruct the full boundary CCFT spectrum through the entanglement Hamiltonian encoded in the ground state. Our work demonstrates how tensor networks are the correct approach to capturing the approximate conformal invariance of weakly first-order phase transitions.

Rec-AD: An Efficient Computation Framework for FDIA Detection Based on Tensor Train Decomposition and Deep Learning Recommendation Model

Authors: Yunfeng Li, Junhong Liu, Zhaohui Yang, Guofu Liao, Chuyun Zhang

arXiv ID: 2507.14668 | Date: 2025-07-19

Abstract: Deep learning models have been widely adopted for False Data Injection Attack (FDIA) detection in smart grids due to their ability to capture unstructured and sparse features. However, the increasing system scale and data dimensionality introduce significant computational and memory burdens, particularly in large-scale industrial datasets, limiting detection efficiency. To address these issues, this paper proposes Rec-AD, a computationally efficient framework that integrates Tensor Train decomposition with the Deep Learning Recommendation Model (DLRM). Rec-AD enhances training and inference efficiency through embedding compression, optimized data access via index reordering, and a pipeline training mechanism that reduces memory communication overhead. Fully compatible with PyTorch, Rec-AD can be integrated into existing FDIA detection systems without code modifications. Experimental results show that Rec-AD significantly improves computational throughput and real-time detection performance, narrowing the attack window and increasing attacker cost. These advancements strengthen edge computing capabilities and scalability, providing robust technical support for smart grid security.

Reconciling Translational Invariance and Hierarchy

Authors: Olai B. Mykland, Zhao Zhang

arXiv ID: 2507.14656 | Date: 2025-07-19

Abstract: Tensor networks are not only numerical tools for describing ground states of quantum many-body systems, but also conceptual aids for understanding their entanglement structures. The proper way to understand tensor networks themselves is through explicit examples of solvable ground states that they represent exactly. In fact, this has historically been how tensor networks for gapped ground states, such as the matrix product state (MPS) and the projected entangled paired state (PEPS), emerged as an elegant analytical framework from numerical techniques like the density matrix renormalization group. However, for gapless ground states, generically described by the multiscale entanglement renormalization ansatz (MERA), a corresponding exactly solvable model has so far been missing. This is because the hierarchical structure of MERA intrinsically breaks the translational invariance. We identify a condition for MERA to be compatible with translational invariance by examining equivalent networks of rank-3 tensors. The condition is satisfied by the previously constructed hierarchical tensor network for the Motzkin and Fredkin chains, which can be considered a non-unitary generalization to the MERA. The hierarchical TN description is complemented by a translationally invariant MPS alternative, which is used to derive the power-law decay of the correlation function and critical exponents of a qq-deformation phase transition.

Quantum State Preparation Based on LimTDD

Authors: Xin Hong, Chenjian Li, Aochu Dai, Sanjiang Li, Shenggang Ying, Mingsheng Ying

arXiv ID: 2507.14496 | Date: 2025-07-19

Abstract: Quantum state preparation is a fundamental task in quantum computing and quantum information processing. With the rapid advancement of quantum technologies, efficient quantum state preparation has become increasingly important. This paper proposes a novel approach for quantum state preparation based on the Local Invertible Map Tensor Decision Diagram (LimTDD). LimTDD combines the advantages of tensor networks and decision diagrams, enabling efficient representation and manipulation of quantum states. Compared with the state-of-the-art quantum state preparation method, LimTDD demonstrates substantial improvements in efficiency when dealing with complex quantum states, while also reducing the complexity of quantum circuits. Examples indicate that, in the best-case scenario, our method can achieve exponential efficiency gains over existing methods. This study not only highlights the potential of LimTDD in quantum state preparation but also provides a robust theoretical and practical foundation for the future development of quantum computing technologies.

Quantum 1/fη1/f^η Noise Induced Relaxation in the Spin-Boson Model

Authors: Florian Otterpohl, Peter Nalbach, Elisabetta Paladino, Giuseppe A. Falci, Michael Thorwart

arXiv ID: 2507.14329 | Date: 2025-07-18

Abstract: We extend the spin-boson model of open quantum systems to the regime of quantum 1/fη1/f^η noise characterized by negative exponents of its spectral distribution. Using the numerically exact time-evolving matrix product operator, we find the dynamic regime diagram, including pseudocoherent dynamics controlled by quantum 1/fη1/f^η noise. We determine the dephasing rate and find for it an empirical formula valid at zero temperature. The bath reorganization energy depends on the infrared bath cutoff frequency, revealing an increased sensitivity of the dephasing on the measurement time of an experiment. \ep{Our results apply to a qubit as an elementary building block of a quantum computer and pave the way towards a quantum treatment of low-frequency noise in more complex architectures.

Irrational CFTs from coupled anyon chains with non-invertible symmetries?

Authors: António Antunes, Junchen Rong

arXiv ID: 2507.14280 | Date: 2025-07-18

Abstract: Irrational CFTs in 1+1d with a discrete spectrum and no conserved currents other than the stress-tensor are expected to be generic, unsolvable by standard methods, and hard to construct explicitly. We introduce a lattice model that realizes a candidate for such a CFT as a conformal phase of matter without fine-tuning. The model is constructed by coupling N3N\geq3 golden anyon chains together, preserving NN copies of the Fibonacci non-invertible symmetry. We use the MPS/DMRG approach to study this model numerically, which allows us to calculate the corresponding conformal data, obtaining hints of its irrationality. Along the way, we characterize the phase diagram for N=2N=2 coupled chains where we identify a weakly first-order phase transition as well as critical points that we are able to identify with known rational CFTs, except for one case. We also provide an extensive list of rational CFTs with 1<c<2.11<c<2.1.

Learning the non-Markovian features of subsystem dynamics

Authors: Michele Coppola, Mari Carmen Bañuls, Zala Lenarčič

arXiv ID: 2507.14133 | Date: 2025-07-18

Abstract: The dynamics of local observables in a quantum many-body system can be formally described in the language of open systems. The problem is that the bath representing the complement of the local subsystem generally does not allow the common simplifications often crucial for such a framework. Leveraging tensor network calculations and optimization tools from machine learning, we extract and characterize the dynamical maps for single- and two-site subsystems embedded in an infinite quantum Ising chain after a global quench. We consider three paradigmatic regimes: integrable critical, integrable non-critical, and chaotic. For each we find the optimal time-local representation of the subsystem dynamics at different times. We explore the properties of the learned time-dependent Liouvillians and whether they can be used to forecast the long-time dynamics of local observables beyond the times accessible through direct quantum many-body numerical simulation. Our procedure naturally suggests a novel measure of non-Markovianity based on the distance between the quasi-exact dynamical map and the closest CP-divisible form and reveals that criticality leads to the closest Markovian representation at large times.

Exploring near critical lattice gauge simulators with Rydberg atoms facilities

Authors: Avi Kaufman, Muhammad Asaduzzaman, Zane Ozzello, Blake Senseman, James Corona, Yannick Meurice

arXiv ID: 2507.14128 | Date: 2025-07-18

Abstract: We motivate the use of a ladder of Rydberg atoms as an analog simulator for a lattice gauge theory version of scalar electrodynamics also called the compact Abelian Higgs model. We demonstrate that by using a few thousand shots from a single copy of the ladder simulator it is possible to estimate the bipartite quantum von Neumann entanglement entropy SAvNS^{vN}_A. The estimation relies on an optimized filtration of the mutual information associated with the bitstrings obtained from public facilities of configurable Rydberg arrays named Aquila. We discuss the limitations associated with finite sampling, sorting fidelity, adiabatic preparation, ramp-down of the Rabi frequency before measurement, and readout errors. We use cumulative probability distribution to compare Aquila results with high accuracy density matrix renormalization group (DMRG) or exact results. The state preparation appears to be the main source of error. We discuss the large volume behavior of the cumulative probability distribution and show examples where for a finite number of shots, there appears to be some large enough size for which, with high probability, any given state is seen at most once. We show that the results presented can be extended to multipartite entanglement. We briefly discuss the cost of the calculations for large square arrays in the context of obtaining quantum advantage in the near future.

Quantifying mixed-state entanglement via partial transpose and realignment moments

Authors: Poetri Sonya Tarabunga, Tobias Haug

arXiv ID: 2507.13840 | Date: 2025-07-18

Abstract: Entanglement plays a crucial role in quantum information science and many-body physics, yet quantifying it in mixed quantum many-body systems has remained a notoriously difficult problem. Here, we introduce families of quantitative entanglement witnesses, constructed from partial transpose and realignment moments, which provide rigorous bounds on entanglement monotones. Our witnesses can be efficiently measured using SWAP tests or variants of Bell measurements, thus making them directly implementable on current hardware. Leveraging our witnesses, we present several novel results on entanglement properties of mixed states, both in quantum information and many-body physics. We develop efficient algorithms to test whether mixed states with bounded entropy have low or high entanglement, which previously was only possible for pure states. We also provide an efficient algorithm to test the Schmidt rank using only two-copy measurements, and to test the operator Schmidt rank using four-copy measurements. Further, our witnesses enable robust certification of quantum circuit depth even in the presence of noise, a task which so far has been limited to noiseless circuits only. Finally, we show that the entanglement phase diagram of Haar random states, quantified by the partial transpose negativity, can be fully established solely by computing our witness, a result that also applies to any state 4-design. Our witnesses can also be efficiently computed for matrix product states, thus enabling the characterization of entanglement in extensive many-body systems. Finally, we make progress on the entanglement required for quantum cryptography, establishing rigorous limits on pseudoentanglement and pseudorandom density matrices with bounded entropy. Our work opens new avenues for quantifying entanglement in large and noisy quantum systems.

Simple ways of preparing qudit Dicke states

Authors: Noah B. Kerzner, Federico Galeazzi, Rafael I. Nepomechie

arXiv ID: 2507.13308 | Date: 2025-07-17

Abstract: Dicke states are permutation-invariant superpositions of qubit computational basis states, which play a prominent role in quantum information science. We consider here two higher-dimensional generalizations of these states: SU(2)SU(2) spin-ss Dicke states and SU(d)SU(d) Dicke states. We present various ways of preparing both types of qudit Dicke states on a qudit quantum computer, using two main approaches: a deterministic approach, based on exact canonical matrix product state representations; and a probabilistic approach, based on quantum phase estimation. The quantum circuits are explicit and straightforward, and are arguably simpler than those previously reported.

Robustness of Magic in the quantum Ising chain via Quantum Monte Carlo tomography

Authors: Hari Timsina, Yi-Ming Ding, Emanuele Tirrito, Poetri Sonya Tarabunga, Bin-Bin Mao, Mario Collura, Zheng Yan, Marcello Dalmonte

arXiv ID: 2507.12902 | Date: 2025-07-17

Abstract: We study the behavior of magic as a bipartite correlation in the quantum Ising chain across its quantum phase transition, and at finite temperature. In order to quantify the magic of partitions rigorously, we formulate a hybrid scheme that combines stochastic sampling of reduced density matrices via quantum Monte Carlo, with state-of-the-art estimators for the robustness of magic - a {\it bona fide} measure of magic for mixed states. This allows us to compute the mutual robustness of magic for partitions up to 8 sites, embedded into a much larger system. We show how mutual robustness is directly related to critical behaviors: at the critical point, it displays a power law decay as a function of the distance between partitions, whose exponent is related to the partition size. Once finite temperature is included, mutual magic retains its low temperature value up to an effective critical temperature, whose dependence on size is also algebraic. This suggests that magic, differently from entanglement, does not necessarily undergo a sudden death.

Scalable tensor network algorithm for quantum impurity problems

Authors: Zhijie Sun, Ruofan Chen, Zhenyu Li, Chu Guo

arXiv ID: 2507.12722 | Date: 2025-07-17

Abstract: The Grassmann time-evolving matrix product operator method has shown great potential as a general-purpose quantum impurity solver, as its numerical errors can be well-controlled and it is flexible to be applied on both the imaginary- and real-time axis. However, a major limitation of it is that its computational cost grows exponentially with the number of impurity flavors. In this work, we propose a multi-flavor extension of it to overcome this limitation. The key insight is that to calculate multi-time correlation functions on one or a few impurity flavors, one could integrate out the degrees of freedom of the rest flavors before hand, which could greatly simplify the calculation. The idea is particularly effective for quantum impurity problems with diagonal hybridization function, i.e., each impurity flavor is coupled to an independent bath, a setting which is commonly used in the field. We demonstrate the accuracy and scalability of our method for the imaginary time evolution of impurity problems with up to three impurity orbitals, i.e., 6 flavors, and benchmark our results against continuous-time quantum Monte Carlo calculations. Our method paves the way of scaling up tensor network algorithms to solve large-scale quantum impurity problems.

Learning mixed quantum states in large-scale experiments

Authors: Matteo Votto, Marko Ljubotina, Cécilia Lancien, J. Ignacio Cirac, Peter Zoller, Maksym Serbyn, Lorenzo Piroli, Benoît Vermersch

arXiv ID: 2507.12550 | Date: 2025-07-16

Abstract: We present and test a protocol to learn the matrix-product operator (MPO) representation of an experimentally prepared quantum state. The protocol takes as an input classical shadows corresponding to local randomized measurements, and outputs the tensors of a MPO which maximizes a suitably-defined fidelity with the experimental state. The tensor optimization is carried out sequentially, similarly to the well-known density matrix renormalization group algorithm. Our approach is provably efficient under certain technical conditions which are expected to be met in short-range correlated states and in typical noisy experimental settings. Under the same conditions, we also provide an efficient scheme to estimate fidelities between the learned and the experimental states. We experimentally demonstrate our protocol by learning entangled quantum states of up to N=96N = 96 qubits in a superconducting quantum processor. Our method upgrades classical shadows to large-scale quantum computation and simulation experiments.

Learning mixed quantum states in large-scale experiments

Authors: Matteo Votto, Marko Ljubotina, Cécilia Lancien, J. Ignacio Cirac, Peter Zoller, Maksym Serbyn, Lorenzo Piroli, Benoît Vermersch

arXiv ID: 2507.12550 | Date: 2025-07-16

Abstract: We present and test a protocol to learn the matrix-product operator (MPO) representation of an experimentally prepared quantum state. The protocol takes as an input classical shadows corresponding to local randomized measurements, and outputs the tensors of a MPO which maximizes a suitably-defined fidelity with the experimental state. The tensor optimization is carried out sequentially, similarly to the well-known density matrix renormalization group algorithm. Our approach is provably efficient under certain technical conditions which are expected to be met in short-range correlated states and in typical noisy experimental settings. Under the same conditions, we also provide an efficient scheme to estimate fidelities between the learned and the experimental states. We experimentally demonstrate our protocol by learning entangled quantum states of up to N=96N = 96 qubits in a superconducting quantum processor. Our method upgrades classical shadows to large-scale quantum computation and simulation experiments.

Higher Structures on Boundary Conformal Manifolds: Higher Berry Phase and Boundary Conformal Field Theory

Authors: Yichul Choi, Hyunsoo Ha, Dongyeob Kim, Yuya Kusuki, Shuhei Ohyama, Shinsei Ryu

arXiv ID: 2507.12525 | Date: 2025-07-16

Abstract: We introduce the notion of higher Berry connection and curvature in the space of conformal boundary conditions in (1+1)d conformal field theories (CFT), related to each other by exactly marginal boundary deformations, forming a "boundary conformal manifold." Our definition builds upon previous works on tensor networks, such as matrix product states (MPS), where the triple inner product or multi-wavefunction overlap plays the key geometric role. On the one hand, our boundary conformal field theory (BCFT) formulation of higher Berry phase provides a new analytic tool to study families of invertible phases in condensed matter systems. On the other hand, it uncovers a new geometric structure on the moduli space of conformal boundary conditions, beyond the usual Riemannian structure defined through the Zamolodchikov metric. When the boundary conformal manifold has an interpretation as the position moduli space of a D-brane, our higher Berry connection coincides with the NS-NS BB-field in string theory. The general definition does not require such an interpretation and is formulated purely field-theoretically, in terms of correlation functions of boundary-condition-changing (bcc) operators. We also explore a connection between higher Berry connections and functional Berry connections in the loop spaces of boundary conformal manifolds.

Spacetime duality between sequential and measurement-feedback circuits

Authors: Tsung-Cheng Lu, Sarang Gopalakrishnan, Yizhi You

arXiv ID: 2507.12523 | Date: 2025-07-16

Abstract: Two prevalent approaches for preparing long-range entangled quantum states are (i) linear-depth sequential unitary (SU) circuits, which apply local unitary gates sequentially, and (ii) constant-depth measurement-feedback (MF) circuits, which employ mid-circuit measurements and conditional feedback based on measurement outcomes. Here, we establish that a broad class of SU and MF circuits are dual to each other under a spacetime rotation. We investigate this spacetime duality in the preparation of various long-range entangled states, including GHZ states, topologically ordered states, and fractal symmetry-breaking states. As an illustration, applying a spacetime rotation to a linear-depth SU circuit that implements a non-invertible Kramers-Wannier duality, originally used to prepare a 1D GHZ state, yields a constant-depth MF circuit that implements a Z2\mathbb{Z}_2 symmetry gauging map, which equivalently prepares the GHZ state. Leveraging this duality, we further propose experimental protocols that require only a constant number of qubits to measure unconventional properties of 1D many-body states. These include (i) measurement of disorder operators, which diagnose the absence of spontaneous symmetry breaking, and (ii) postselection-free detection of measurement-induced long-range order, which emerges in certain symmetry-protected topological phases. We also show that measurement-induced long-range order provides a lower bound for strange correlators, which may be of independent interest.

QAS-QTNs: Curriculum Reinforcement Learning-Driven Quantum Architecture Search for Quantum Tensor Networks

Authors: Siddhant Dutta, Nouhaila Innan, Sadok Ben Yahia, Muhammad Shafique

arXiv ID: 2507.12013 | Date: 2025-07-16

Abstract: Quantum Architecture Search (QAS) is an emerging field aimed at automating the design of quantum circuits for optimal performance. This paper introduces a novel QAS framework employing hybrid quantum reinforcement learning with quantum curriculum learning strategies, enabling learning agents to tackle increasingly complex quantum circuit design tasks. We benchmark four state-of-the-art classical reinforcement learning algorithms (A2C, PPO, DDQN, TD3) against their quantum-enhanced counterparts (QA2C, QPPO, QDDQN, QTD3) for optimizing variational quantum circuits (VQCs). Our approach progressively increases circuit depth and gate complexity during training, leveraging parameterized quantum circuits as function approximations. To improve learning efficiency and stability, all algorithms, both classical and quantum, are augmented with Prioritized Experience Replay (PER). Experimental results show that quantum-enhanced RL significantly outperforms classical methods. In a 2-qubit environment, PERQDDQN achieves a success probability of 0.46 with ~3,000 optimal successes, surpassing classical PERDDQN (0.42, ~2,400). In the more complex 3-qubit setting, PERQDDQN and PERQTD3 reach success probabilities of ~0.47, with optimal success counts of ~3,800 and ~3,600, respectively, outperforming their classical counterparts. Additionally, we apply our QAS-QTN approach to a classification problem, where the optimized quantum circuit achieves an accuracy of 90.33\%, outperforming quantum models consisting of random ansatz. This hybrid classical-quantum approach leads to faster convergence and more efficient quantum circuit designs, demonstrating its potential for advancing automated quantum architecture search.

Fractal Path Strategies for Efficient 2D DMRG Simulations

Authors: Oliver R. Bellwood, Heitor P. Casagrande, William J. Munro

arXiv ID: 2507.11820 | Date: 2025-07-16

Abstract: Numerical simulations of quantum magnetism in two spatial dimensions are often constrained by the area law of entanglement entropy, which heavily limits the accessible system sizes in tensor network methods. In this work, we investigate how the choice of mapping from a two-dimensional lattice to a one-dimensional path affects the accuracy of the two-dimensional Density Matrix Renormalization Group algorithm. We systematically evaluate all mappings corresponding to a subset of the Hamiltonian paths of the N×NN \times N grid graphs up to N=8N=8 and demonstrate that the fractal space-filling curves generally lead to faster convergence in ground state searches compared to the commonly used ``snake" path. To explain this performance gain, we analyze various locality metrics and propose a scalable method for constructing high-performing paths on larger lattices by tiling smaller optimal paths. Our results show that such paths consistently improve simulation convergence, with the advantage increasing with system size.

Simulating and Sampling from Quantum Circuits with 2D Tensor Networks

Authors: Manuel S. Rudolph, Joseph Tindall

arXiv ID: 2507.11424 | Date: 2025-07-15

Abstract: Classical simulations of quantum circuits play a vital role in the development of quantum computers and for taking the temperature of the field. Here, we classically simulate various physically-motivated circuits using 2D tensor network ansätze for the many-body wavefunction which match the geometry of the underlying quantum processor. We then employ a generalized version of the boundary Matrix Product State contraction algorithm to controllably generate samples from the resultant tensor network states. Our approach allows us to systematically converge both the quality of the final state and the samples drawn from it to the true distribution defined by the circuit, with GPU hardware providing us with significant speedups over CPU hardware. With these methods, we simulate the largest local unitary Jastrow ansatz circuit taken from recent IBM experiments to numerical precision. We also study a domain-wall quench in a two-dimensional discrete-time Heisenberg model on large heavy-hex and rotated square lattices, which reflect IBM's and Google's latest quantum processors respectively. We observe a rapid buildup of complex loop correlations on the Google Willow geometry which significantly impact the local properties of the system. Meanwhile, we find loop correlations build up extremely slowly on heavy-hex processors and have almost negligible impact on the local properties of the system, even at large circuit depths. Our results underscore the role the geometry of the quantum processor plays in classical simulability.

Diagnosing phase transitions through time scale entanglement

Authors: Stefan Rohshap, Hirone Ishida, Frederic Bippus, Anna Kauch, Karsten Held, Hiroshi Shinaoka, Markus Wallerberger

arXiv ID: 2507.11276 | Date: 2025-07-15

Abstract: Spatial entanglement of wave functions has matured into an enthralling and very active research area. Here, we unearth a completely different kind of entanglement, the entanglement between different time scales. This is feasible through quantics tensor train diagnostics (QTTD), wherein the bond dimension for an nn-particle correlation function allows diagnosing the temporal entanglement. As examples, we study time-scale entanglement of the Hubbard dimer, the four-site Hubbard ring with and without next-nearest neighbor hopping and the single-impurity Anderson model. Besides introducing the QTTD method, our major finding is that the time-scale entanglement is generically maximal at phase transitions and crossovers. This is independent of the correlation function studied. Thus, QTTD is a universal tool for detecting quantum phase transitions, ground state crossings in finite systems, and thermal crossovers.

Interpretable Bayesian Tensor Network Kernel Machines with Automatic Rank and Feature Selection

Authors: Afra Kilic, Kim Batselier

arXiv ID: 2507.11136 | Date: 2025-07-15

Abstract: Tensor Network (TN) Kernel Machines speed up model learning by representing parameters as low-rank TNs, reducing computation and memory use. However, most TN-based Kernel methods are deterministic and ignore parameter uncertainty. Further, they require manual tuning of model complexity hyperparameters like tensor rank and feature dimensions, often through trial-and-error or computationally costly methods like cross-validation. We propose Bayesian Tensor Network Kernel Machines, a fully probabilistic framework that uses sparsity-inducing hierarchical priors on TN factors to automatically infer model complexity. This enables automatic inference of tensor rank and feature dimensions, while also identifying the most relevant features for prediction, thereby enhancing model interpretability. All the model parameters and hyperparameters are treated as latent variables with corresponding priors. Given the Bayesian approach and latent variable dependencies, we apply a mean-field variational inference to approximate their posteriors. We show that applying a mean-field approximation to TN factors yields a Bayesian ALS algorithm with the same computational complexity as its deterministic counterpart, enabling uncertainty quantification at no extra computational cost. Experiments on synthetic and real-world datasets demonstrate the superior performance of our model in prediction accuracy, uncertainty quantification, interpretability, and scalability.

An Optimization-Free Recursive QAOA for the Binary Paint Shop Problem

Authors: Gary J Mooney, Jedwin Villanueva, Bhaskar Roy Radhan, Joydip Ghosh, Charles D Hill, Lloyd C L Hollenberg

arXiv ID: 2507.10908 | Date: 2025-07-15

Abstract: The classical outer optimisation loop of the classical-quantum hybrid Quantum Approximate Optimisation Algorithm (QAOA) can be bypassed by transferring precomputed parameters to larger unseen problem instances using the parameter concentration property found in certain classes of problem instances. In this paper, parameter transfer is applied to the recursive-QAOA (RQAOA) approach of Bravyi et al. implementing the Binary Paint Shop Problem (BPSP) -- an optimisation problem found in manufacturing where a sequence of cars are to be painted under certain constraints while minimising the number of colour changes between cars. The BPSP can be conveniently formulated as an Ising ground state problem with a symmetric Hamiltonian and Ising graph structure that is well-suited for QAOA parameter-transfer techniques. Throughout our quantum simulated experiments, parameter transfer showed no noticeable reduction in solution quality over optimisation for QAOA and RQAOA while substantially improving the efficiency due to avoiding measurements required for optimisation. Additionally, RQAOA only requires measurements of ZZZZ-correlations instead of full statevectors, benefiting from the reverse-causal-cone feature that leads to circuits with significantly lower CNOT counts and depths. The performance of QAOA and RQAOA with parameter transfer is benchmarked against classical solvers and heuristics and their resilience to non-optimal parameters is explored. The entanglement entropy and bond dimensions are obtained from matrix product state simulations to provide an indication of the classical resources required to simulate the quantum algorithms. Circuit sizes and measurement counts are compared between the implementations.

Natural super-orbitals representation of many-body operators

Authors: Maxime Debertolis

arXiv ID: 2507.10690 | Date: 2025-07-14

Abstract: We introduce the concept of natural super-orbitals for many-body operators, defined as the eigenvectors of the one-body super-density matrix associated with a vectorized operator. We relate these objects to measures of non-Gaussianity of operators associated to the occupations of the natural super-orbitals, and define how the non-stabilizerness of operators can be affected by such a basis rotation. We first analyze the general analytical properties of these objects in various contexts, including the time-evolution operator of non-interacting Hamiltonians and Haar-random unitaries. We then perform a numerical investigation of the natural super-orbitals corresponding to both the time-evolution operator and a time-evolved local operator, focusing on two many-body systems: the fermionic t-Vt\text{-}V chain and an impurity model, using tensor network simulations. Our results reveal that the t-Vt\text{-}V model lacks a preferred super-orbital basis, while in the impurity model, the occupations of the natural orbitals for both operators decay exponentially at all times. This indicates that only a small number of orbitals contribute significantly to quantum correlations, enabling a compact matrix-product-operator representation and a reduced non-stabilizerness in the natural orbital basis. Finally, we examine the spatial spread of the natural orbitals for time-evolved local operators in the impurity model and show that the complexity of this operator in the natural orbital basis saturates over time. This new framework opens the door to future research that leverages the compressed structure of operators in their natural super-orbital basis, enabling for instance the computation of out-of-time-order correlators in large interacting systems over extended time scales.

Understanding the Rank of Tensor Networks via an Intuitive Example-Driven Approach

Authors: Wuyang Zhou, Giorgos Iacovides, Kriton Konstantinidis, Ilya Kisil, Danilo Mandic

arXiv ID: 2507.10170 | Date: 2025-07-14

Abstract: Tensor Network (TN) decompositions have emerged as an indispensable tool in Big Data analytics owing to their ability to provide compact low-rank representations, thus alleviating the ``Curse of Dimensionality'' inherent in handling higher-order data. At the heart of their success lies the concept of TN ranks, which governs the efficiency and expressivity of TN decompositions. However, unlike matrix ranks, TN ranks often lack a universal meaning and an intuitive interpretation, with their properties varying significantly across different TN structures. Consequently, TN ranks are frequently treated as empirically tuned hyperparameters, rather than as key design parameters inferred from domain knowledge. The aim of this Lecture Note is therefore to demystify the foundational yet frequently misunderstood concept of TN ranks through real-life examples and intuitive visualizations. We begin by illustrating how domain knowledge can guide the selection of TN ranks in widely-used models such as the Canonical Polyadic (CP) and Tucker decompositions. For more complex TN structures, we employ a self-explanatory graphical approach that generalizes to tensors of arbitrary order. Such a perspective naturally reveals the relationship between TN ranks and the corresponding ranks of tensor unfoldings (matrices), thereby circumventing cumbersome multi-index tensor algebra while facilitating domain-informed TN design. It is our hope that this Lecture Note will equip readers with a clear and unified understanding of the concept of TN rank, along with the necessary physical insight and intuition to support the selection, explainability, and deployment of tensor methods in both practical applications and educational contexts.

Intertwined charge, spin, and orbital degrees of freedom under electronic correlations in the one-dimensional Fe3+^{3+} chalcogenide chain

Authors: Yang Zhang, Pontus Laurell, Gonzalo Alvarez, Adriana Moreo, Thomas A. Maier, Ling-Fang Lin, Elbio Dagotto

arXiv ID: 2507.09870 | Date: 2025-07-14

Abstract: Motivated by recent developments in the study of quasi-one-dimensional iron systems with Fe2+^{2+}, we comprehensively study the Fe3+^{3+} chalcogenide chain system. Based on first-principles calculations, the Fe3+^{3+} chain has a similar electronic structure as discussed before in the iron 2+ chain, due to similar FeX4X_4 (XX = S or Se) tetrahedron chain geometry. Furthermore, a three-orbital electronic Hubbard model for this chain was constructed by using the density matrix renormalization group method. A robust antiferromagnetic coupling was unveiled in the chain direction. In addition, in the intermediate electronic correlation U/WU/W region, we found an interesting orbital-selective Mott phase with the coexistence of localized and itinerant electrons (UU is the on-site Hubbard repulsion, while WW is the electronic bandwidth). Furthermore, we do not observe any obvious pairing tendency in the Fe3+^{3+} chain in the electronic correlation U/WU/W region, where superconducting pairing tendencies were reported before in iron ladders. This suggests that superconductivity is unlikely to emerge in the Fe3+^{3+} systems. Our results establish with clarity the similarities and differences between Fe2+^{2+}and Fe3+^{3+} iron chains, as well as iron ladders.

Emergent Distance and Metricity of Mutual Information in 1D Quantum Chains

Authors: Beau Leighton-Trudel

arXiv ID: 2507.09749 | Date: 2025-07-13

Abstract: We develop and formalize a phase diagnostic based on the information-distance \(d_E = K_0/\sqrt{I}\) (mutual information \(I\)) for 1D quantum chains. Calibrating with the Euclidean benchmark \(I(r)\propto r^{-2}\mapsto d_E(r)\propto r\) makes the triangle-inequality test parameter-free and scale-invariant. Under site-averaged, monotone scaling conditions on the 1D line we establish a criterion linking the decay of \(I(r)\) to metric behavior of \(d_E(r)\): power laws \(I(r)\sim r^{-X}\) with \(0

Tensor train representations of Greeks for Fourier-based pricing of multi-asset options

Authors: Rihito Sakurai, Koichi Miyamoto, Tsuyoshi Okubo

arXiv ID: 2507.08482 | Date: 2025-07-11

Abstract: Efficient computation of Greeks for multi-asset options remains a key challenge in quantitative finance. While Monte Carlo (MC) simulation is widely used, it suffers from the large sample complexity for high accuracy. We propose a framework to compute Greeks in a single evaluation of a tensor train (TT), which is obtained by compressing the Fourier transform (FT)-based pricing function via TT learning using tensor cross interpolation. Based on this TT representation, we introduce two approaches to compute Greeks: a numerical differentiation (ND) approach that applies a numerical differential operator to one tensor core and an analytical (AN) approach that constructs the TT of closed-form differentiation expressions of FT-based pricing. Numerical experiments on a five-asset min-call option in the Black-Sholes model show significant speed-ups of up to about 105×10^{5} \times over MC while maintaining comparable accuracy. The ND approach matches or exceeds the accuracy of the AN approach and requires lower computational complexity for constructing the TT representation, making it the preferred choice.

Symmetry-based theory of Dirac fermions on two-dimensional hyperbolic crystals: Coupling to the spin connection

Authors: Ana Djordjević, Marija Dimitrijević Ćirić, Vladimir Juričić

arXiv ID: 2507.08276 | Date: 2025-07-11

Abstract: Discrete fermionic and bosonic models for hyperbolic lattices have attracted significant attention across a range of fields since the experimental realization of hyperbolic lattices in metamaterial platforms, sparking the development of hyperbolic crystallography. However, a fundamental and experimentally consequential aspect remains unaddressed: fermions propagating in curved space inherently couple to the underlying geometry via the spin connection, as required by general covariance - a feature not yet incorporated in studies of hyperbolic crystals. Here, we introduce a symmetry-based framework for Dirac fermions on two-dimensional hyperbolic lattices, explicitly incorporating spin-curvature coupling via a discrete spin connection. Starting from the continuous symmetries of the Poincaré disk, we classify the irreducible representations and construct a symmetry-adapted basis, establishing a direct correspondence to the continuum Dirac theory. We show that this continuum theory predicts a finite density of states at zero energy for any finite curvature in DD-dimensional hyperbolic space with 2D42\leq D \leq 4, suggesting enhanced susceptibility of Dirac fermions to interaction-driven instabilities at weak coupling. We then derive explicit forms of discrete translational and rotational symmetries for lattices characterized by Schläfli symbols {p,q}\{p,q\}, and explicitly construct the discrete spin connection, represented as hopping phases, via parallel transport. Our results pave the way for experimental realization of spin-curvature effects in metamaterial platforms and systematic numerical studies of correlated Dirac phases in hyperbolic geometries.

Real-Time Dynamics in a (2+1)-D Gauge Theory: The Stringy Nature on a Superconducting Quantum Simulator

Authors: Jesús Cobos, Joana Fraxanet, César Benito, Francesco di Marcantonio, Pedro Rivero, Kornél Kapás, Miklós Antal Werner, Örs Legeza, Alejandro Bermudez, Enrique Rico

arXiv ID: 2507.08088 | Date: 2025-07-10

Abstract: Understanding the confinement mechanism in gauge theories and the universality of effective string-like descriptions of gauge flux tubes remains a fundamental challenge in modern physics. We probe string modes of motion with dynamical matter in a digital quantum simulation of a (2+1) dimensional gauge theory using a superconducting quantum processor with up to 144 qubits, stretching the hardware capabilities with quantum-circuit depths comprising up to 192 two-qubit layers. We realize the Z2Z_2-Higgs model (Z2Z_2HM) through an optimized embedding into a heavy-hex superconducting qubit architecture, directly mapping matter and gauge fields to vertex and link superconducting qubits, respectively. Using the structure of local gauge symmetries, we implement a comprehensive suite of error suppression, mitigation, and correction strategies to enable real-time observation and manipulation of electric strings connecting dynamical charges. Our results resolve a dynamical hierarchy of longitudinal oscillations and transverse bending at the end points of the string, which are precursors to hadronization and rotational spectra of mesons. We further explore multi-string processes, observing the fragmentation and recombination of strings. The experimental design supports 300,000 measurement shots per circuit, totaling 600,000 shots per time step, enabling high-fidelity statistics. We employ extensive tensor network simulations using the basis update and Galerkin method to predict large-scale real-time dynamics and validate our error-aware protocols. This work establishes a milestone for probing non-perturbative gauge dynamics via superconducting quantum simulation and elucidates the real-time behavior of confining strings.

Diagonal Isometric Form for Tensor Product States in Two Dimensions

Authors: Benjamin Sappler, Masataka Kawano, Michael P Zaletel, Frank Pollmann

arXiv ID: 2507.08080 | Date: 2025-07-10

Abstract: Isometric tensor product states (isoTPS) generalize the isometric form of the one-dimensional matrix product states (MPS) to tensor networks in two and higher dimensions. Here, we introduce an alternative isometric form for isoTPS by incorporating auxiliary tensors to represent the orthogonality hypersurface. We implement the time evolving block decimation (TEBD) algorithm on this new isometric form and benchmark the method by computing ground states and the real time evolution of the transverse field Ising model in two dimensions on large square lattices of up to 1250 sites. Our results demonstrate that isoTPS can efficiently capture the entanglement structure of two-dimensional area law states. The short-time dynamics is also accurately reproduced even at the critical point. Our isoTPS formulation further allows for a natural extension to different lattice geometries, such as the honeycomb or kagome latice.

Chiral superconductivity near a fractional Chern insulator

Authors: Taige Wang, Michael P. Zaletel

arXiv ID: 2507.07921 | Date: 2025-07-10

Abstract: Superconductivity arising from fully spin-polarized, repulsively interacting electrons can host intrinsically chiral Cooper pairs and Majorana zero modes, yet no concrete microscopic route to such a state has been established. Motivated by recent observations in twisted homobilayer MoTe2_2 and rhombohedral pentalayer graphene, where fractional Chern insulators (FCIs) appear adjacent to spin-valley-polarized superconductors, we investigate a minimal model: spinless electrons in the lowest Landau level subject to a tunable periodic potential. Large-scale density-matrix renormalization group (DMRG) calculations reveal that, as the FCI gap closes, two nearly degenerate phases emerge before the system turns metallic: a chiral ff-wave superconductor and a 3×3\sqrt{3} \times \sqrt{3} charge-density wave (CDW) whose energies differ by less than 1%1\%. These two competing states mirror the superconducting and re-entrant integer quantum Hall (RIQH) phases observed experimentally near the FCI regime. The superconducting dome survives realistic Coulomb interaction, light doping, and various lattice geometry. Melting the FCI therefore provides a new mechanism for realizing spin-polarized chiral superconductivity and RIQH order. We predict that twisted MoTe2_2 at larger twist angles will develop a superconducting dome even at filling ν=2/3ν= 2/3, and suppressing this superconductivity with a magnetic field should drive the system into an RIQH state.

Quench spectroscopy for Lieb-Liniger bosons in the presence of harmonic trap

Authors: Jiachen Yu, Yuanzhe Hu, Wenhan Chen, Jianing Yang, Xuzong Chen, Hepeng Yao

arXiv ID: 2507.07699 | Date: 2025-07-10

Abstract: Quench spectroscopy has emerged as a novel and powerful technique for probing the energy spectrum of various quantum phases for quantum systems from out-of-equilibrium dynamics. While its efficacy has been demonstrated in the homogeneous systems theoretically, most experimental setups feature a confining potential, such as a harmonic trap, which complicates the practical implementations. In this work, we experimentally probe the quench spectroscopy for one-dimensional bosons in optical lattices with the presence of a harmonic trap, and comparing our results with the density matrix renormalization group simulation. For the Mott insulator phase, although a gap is still observed, the band signal is broadened along the frequency space and cut at the half Brillouin zone, which can be explained by the nearest-neighbor tunneling excitations under harmonic confinement. Comparing with the superfluid spectrum, we can see a clear distinction between the two phases and find the inverse quench with larger amplitude yields the clearest spectrum. Our work offers pivotal insights into conducting quench spectroscopy effectively in practical systems.

Extracting Nonlinear Dynamical Response Functions from Time Evolution

Authors: Atsushi Ono

arXiv ID: 2507.07679 | Date: 2025-07-10

Abstract: We develop a general framework based on the functional derivative to extract nonlinear dynamical response functions from the temporal evolution of physical quantities, without explicitly computing multipoint correlation functions. We validate our approach by calculating the second- and third-order optical responses in the Rice-Mele model and further apply it to a many-body interacting system using a tensor network method. This framework is broadly applicable to any method that can compute real-time dynamics, offering a powerful and versatile tool for investigating nonlinear responses in dynamical systems.

Summing Real Time Feynman Paths of Lattice Polaron with Matrix Product States

Authors: Qi Gao, Yuan Wan

arXiv ID: 2507.07648 | Date: 2025-07-10

Abstract: We study numerically the real time dynamics of lattice polarons by combining the Feynman path integral and the matrix product state (MPS) approach. By constructing and solving a flow equation, we show that the integrand, viewed as a multivariable function of polaron world line parameters, can be compressed as a low bond dimension MPS, thereby allowing for efficient evaluation of various dynamical observables. We establish the effectiveness of our method by benchmarking the calculated polaron spectral function in one dimension against available results. We further demonstrate its potential by presenting the polaron spectral function in two dimensions and simulating polaron diffusion in both one and two dimensions.

Tangent Space Excitation Ansatz for Quantum Circuits

Authors: Ji-Yao Chen, Bochen Huang, D. L. Zhou, Norbert Schuch, Chenfeng Cao, Muchun Yang

arXiv ID: 2507.07646 | Date: 2025-07-10

Abstract: Computing the excitation spectra of quantum many-body systems on noisy quantum devices is a promising avenue to demonstrate the practical utility of current quantum processors, especially as we move toward the ``megaquop'' regime. For this task, here we introduce a \textit{tangent-space excitation ansatz} for quantum circuits, motivated by the quasi-particle picture of many-body systems and the structural similarity between quantum circuits and classical tensor networks. Increasing the circuit depth by one layer to construct the tangent space around the variational optimum of a parametrized quantum circuit, we show that a large number of low-energy states can be accurately captured. We demonstrate this ansatz using various models in both one and two spatial dimensions, including the challenging kagome Heisenberg antiferromagnet. We further provide evidence that this approach, implementable using Hadamard test, is stable in the presence of measurement noise and scalable to large system size.

Emergent QED3_3 at the bosonic Laughlin state to superfluid transition

Authors: Taige Wang, Xue-Yang Song, Michael P. Zaletel, T. Senthil

arXiv ID: 2507.07611 | Date: 2025-07-10

Abstract: Quantum phase transitions between topologically ordered and symmetry-broken phases lie beyond Landau theory. A prime example is the conjectured continuous transition from the bosonic ν=1/2ν= 1/2 Laughlin state to a superfluid, proposed to be governed by a QED3_3--Chern--Simons (CS) critical point whose stability remains uncertain. We study half-filled bosons in the lowest Landau level subject to a lattice potential. Infinite-cylinder DMRG reveals a single continuous Laughlin--to--superfluid transition. Adiabatic flux insertion collapses the many-body gap and exposes massless Dirac quasiparticles, while momentum-resolved correlation lengths show that three lattice-related density modes share the same critical exponent, evidencing an emergent SO(3)SO(3) symmetry. The joint appearance of Dirac dispersion and symmetry enlargement provides microscopic support for a stable QED3_3--CS fixed point. Our numerical strategy also offers a blueprint for exploring Landau-forbidden transitions in fractional Chern insulators and composite Fermi liquids realised in moire and cold-atom systems.

Evolution from intralayer to interlayer superconductivity in a bilayer tt-JJ model

Authors: Yuan Yang, Xin Lu, Yuan Wan, Wei-Qiang Chen, Shou-Shu Gong

arXiv ID: 2507.07545 | Date: 2025-07-10

Abstract: Motivated by the bilayer cuprate superconductors and nickelate superconductor La3_3Ni2_2O7_7, we investigate the evolution from intralayer to interlayer superconductivity based on a bilayer two-leg tt-JJ-JJ_{\bot} model, where tt is the in-plane electron hopping, JJ is the in-plane spin interaction, and JJ_{\bot} is the inter-plane spin interaction. By means of the density matrix renormalization group calculations, we obtain the quantum phase diagram of the system by tuning JJ_{\bot} in a large doping range δ=1/81/2δ= 1/8 - 1/2. We find that a large JJ_{\bot} can always drive an interlayer superconductivity by coupling the two layers in both the Luther-Emery liquid and Luttinger liquid states. By coupling two Luther-Emery liquid states, the in-plane superconductivity evolves to inter-plane superconductivity either through an intermediate charge density wave (CDW) phase or directly, depending on doping ratio. This emergent CDW phase, which exists over a finite doping range, appears to develop from the CDW state of the two-leg ladder at δ=1/4δ= 1/4. By coupling two Luttinger liquids, the in-plane Luttinger liquids show a transition to the inter-plane superconducting phase at large JJ_{\bot}, as reported in previous literature. Interestingly, in the intermediate JJ_{\bot} regime we find that while the in-plane Luttinger-liquid features remain stable, the inter-plane superconductivity can develop an enhanced quasi-long-range order with the power exponent KSCzz1K^{zz}_{\rm SC} \sim 1. At last, we show that the interlayer superconductivity is also stable by coupling the bilayer three-leg tt-JJ ladders by a strong JJ_{\bot} interaction, from both the Luther-Emery liquid and Luttinger-liquid states.

Finitely Correlated States Driven by Topological Dynamics

Authors: Eric B. Roon, Jeffrey H. Schenker

arXiv ID: 2507.07287 | Date: 2025-07-09

Abstract: Let (Ω,)(Ω, ¶) be a standard probability space and let ϑ:ΩΩ\vartheta:Ω\to Ω be a measure preserving ergodic homeomorphism. Let A\mathcal{A} be a CC^*-algebra with a unit and let AZ\mathcal{A}_{\mathbb{Z}} be the quasi-local algebra associated to the spin chain with one-site algebra A\mathcal{A}. Equip AZ\mathcal{A}_{\mathbb{Z}} with the group action of translation by kk-units, τkAut(AZ)τ_k\in Aut(\mathcal{A}_{\mathbb{Z}}) for kZk\in \mathbb{Z}. We study the problem of finding a disordered matrix product state decomposition for disordered states ψ(ω)ψ(ω) on AZ\mathcal{A}_{\mathbb{Z}} with the covariance symmetry condition ψ(ω)τk=ψ(ϑkω)ψ(ω) \circ τ_k = ψ(\vartheta^k ω). This can be seen as an ergodic generalization of the results of Fannes, Nachtergaele, and Werner \cite{FannesNachtergaeleWerner}. To reify our structure theory, we present a disordered state νων_ω obtained by sampling the AKLT model \cite{AKLT} in parameter space. We go on to show that νων_ω has a nearest-neighbor parent Hamiltonian, its bulk spectral gap closes, but it has almost surely exponentially decaying correlations, and finally, that νων_ω is time-reversal symmetry protected with a Tasaki index of 1-1.

Energy Spectra of Compressed Quantum States

Authors: Daochen Wang

arXiv ID: 2507.07191 | Date: 2025-07-09

Abstract: Quantum algorithms for estimating the ground state energy of a quantum system often operate by preparing a classically accessible quantum state and then applying quantum phase estimation. Whether this approach yields quantum advantage hinges on the state's energy spectrum, that is, the sequence of the state's overlaps with the energy eigenstates of the system Hamiltonian. For any entanglement-compressed quantum state with minimal expected energy, it is shown that its energy spectrum decays at most with the inverse-squared energy eigenvalues. This explains the main empirical finding of Silvester, Carleo, and White (Physical Review Letters, 2025) that the energy spectra of matrix product states do not decay exponentially. It also reduces the question of quantum advantage to the energy and entanglement profile of the Hamiltonian's eigenstates.

Majorana edge reconstruction and the ν=5/2ν=5/2 non-Abelian thermal Hall puzzle

Authors: Tevž Lotrič, Taige Wang, Michael P. Zaletel, Steven H. Simon, S. A. Parameswaran

arXiv ID: 2507.07161 | Date: 2025-07-09

Abstract: Pioneering thermal transport measurements on two-dimensional electron gases in high magnetic fields have demonstrated that the quantized Hall state at filling factor ν=5/2ν=5/2 has a thermal Hall conductance κκ quantized in half-integer multiples of κ0=π2kB2T/3hκ_0 = {π^2 k_B^2 T}/{3h}. Half-integer κ/κ0κ/κ_0 is a signature of neutral Majorana edge modes, in turn linked to the presence of non-Abelian anyon excitations in the bulk. However, the experimentally observed value of κκ corresponds to the 'PH-Pfaffian' state, in tension with numerical studies which instead favor either the Pfaffian or the AntiPfaffian. A variety of mechanisms have been invoked to explain this discrepancy, but have been either ruled out by further experiments or else involve fine-tuning. Building on density-matrix-renormalization group studies of physically realistic edges and analytic calculations of edge structure, we propose an alternative resolution of this puzzle involving an 'edge reconstruction' solely involving the neutral Majorana sector of the theory. Such a Majorana edge reconstruction can "screen'' a Pfaffian or AntiPfaffian bulk, so that transport signatures become indistinguishable from those of the PH-Pfaffian. We argue that this physically natural scenario is consistent with experiment.

Utility-Scale Quantum Computation of Ground-State Energy in a 100+ Site Planar Kagome Antiferromagnet via Hamiltonian Engineering

Authors: Muhammad Ahsan

arXiv ID: 2507.06361 | Date: 2025-07-08

Abstract: We present experimental quantum computation of the ground-state energy in a 103-site flat Kagome lattice under the antiferromagnetic Heisenberg model (KAFH), with IBM's Heron r1 and Heron r2 quantum processors. For spin-1/2 KAFH, our per-site ground-state energy estimate is 0.417J-0.417\,J, which, under open-boundary corrections, matches the energy in the thermodynamic limit, i.e., 0.4386J-0.4386\,J. To achieve this, we used a hybrid approach that splits the conventional Variational Quantum Eigensolver (VQE) into local (classical) and global (quantum) components for efficient hardware utilization. More importantly, we introduce a Hamiltonian engineering strategy that increases coupling on defect triangles to mimic loop-flip dynamics, allowing us to simplify the ansatz while retaining computational accuracy. Using a single-repetition, hardware-efficient ansatz, we entangle up to 103 qubits with high fidelity to determine the Hamiltonian's lowest eigenvalue. This work demonstrates the scalability of VQE for frustrated 2D systems and lays the foundation for future studies using deeper ansatz circuits and larger lattices on utility quantum processors.

Matrix-product entanglement characterizing the optimality of state-preparation quantum circuits

Authors: Shuo Qi, Wen-Jun Li, Gang Su, Shi-Ju Ran

arXiv ID: 2507.05989 | Date: 2025-07-08

Abstract: Multipartite entanglement offers a powerful framework for understanding the complex collective phenomena in quantum many-body systems that are often beyond the description of conventional bipartite entanglement measures. Here, we propose a class of multipartite entanglement measures that incorporate the matrix product state (MPS) representation, enabling the characterization of the optimality of quantum circuits for state preparation. These measures are defined as the minimal distances from a target state to the manifolds of MPSs with specified virtual bond dimensions χχ, and thus are dubbed as χχ-specified matrix product entanglement (χχ-MPE). We demonstrate superlinear, linear, and sublinear scaling behaviors of χχ-MPE with respect to the negative logarithmic fidelity FF in state preparation, which correspond to excessive, optimal, and insufficient circuit depth DD for preparing χχ-virtual-dimensional MPSs, respectively. Specifically, a linearly-growing χχ-MPE with FF suggests HχHD\mathcal{H}_χ \simeq \mathcal{H}_{D}, where Hχ\mathcal{H}_χ denotes the manifold of the χχ-virtual-dimensional MPSs and HD\mathcal{H}_{D} denotes that of the states accessible by the DD layer circuits. We provide an exact proof that Hχ=2HD=1\mathcal{H}_{χ=2} \equiv \mathcal{H}_{D=1}. Our results establish tensor networks as a powerful and general tool for developing parametrized measures of multipartite entanglement. The matrix product form adopted in χχ-MPE can be readily extended to other tensor network ansätze, whose scaling behaviors are expected to assess the optimality of quantum circuit in preparing the corresponding tensor network states.

Hierarchical Wavepacket Propagation Framework via ML-MCTDH for Molecular Reaction Dynamics

Authors: Xingyu Zhang, Qingyong Meng

arXiv ID: 2507.05593 | Date: 2025-07-08

Abstract: This work presents a computational framework for studying reaction dynamics via wavepacket propagation, employing the multiconfiguration time-dependent Hartree (MCTDH) method and its multilayer extension (ML-MCTDH) as the core methodologies. The core idea centers on the concept of modes that combine several coordinates along with their hierarchical separations because the degrees of freedom are too numerous to be efficiently treated as a single mode. First, the system is partitioned into several fragments within the same layer, and these fragments are further decomposed. Repeating this process, a hierarchical separation of modes emerges, until modes of a manageable size are achieved. Accordingly, the coordinates frame can be designed hierarchically. Second, the kinetic energy operator (KEO) is derived as a sum-of-products (SOP) of single-particle differential operators through polyspherical approach, while the potential energy surface (PES) is expressed in a similar SOP form of single-particle potentials (SPPs) through (1) reconstruction approaches using an existing PES or (2) direct approaches based on a computed database. Third, the nuclear wave function is expressed in a multi-layer expansion form, where each term is a product of single-particle functions (SPFs) that are further expanded by the SPFs in deeper layer. This expansion form is also adopted by variational eigensolver for electronic wave function. Finally, the Dirac-Frenkel variational principle leads to a set of working equations whose solutions reproduce reaction dynamics. In addition, the hierarchical framework can be rearranged by the mathematical language of tensor network (TN) or tree tensor network (TTN). In this work, we compare the methods represented by function with those in the form of TN or TTN. We also discuss the limitations of the present framework and propose solutions, providing further perspectives.

Tensor network algorithm to solve polaron impurity problems

Authors: Ruofan Chen, Lei Gu, Chu Guo

arXiv ID: 2507.05580 | Date: 2025-07-08

Abstract: The polaron problem is a very old problem in condensed matter physics that dates back to the thirties, but still remain largely unsolved today, especially when electron-electron interaction is taken into consideration. The presence of both electron-electron and electron-phonon interactions in the problem invalidates most existing numerical methods, either computationally too expensive or simply intractable. The continuous time quantum Monte Carlo (CTQMC) methods could tackle this problem, but are only effective in the imaginary-time axis. In this work we present a method based on tensor network and the path integral formalism to solve polaron impurity problems. As both the electron and phonon baths can be integrated out via the Feynman-Vernon influence functional in the path integral formalism, our method is free of bath discretization error. It can also flexibly work on the imaginary, Keldysh, and the L-shaped Kadanoff contour. In addition, our method can naturally resolve several long-existing challenges: (i) non-diagonal hybridization function; (ii) measuring multi-time correlations beyond the single particle Green's functions. We demonstrate the effectiveness and accuracy of our method with extensive numerical examples against analytic solutions, exact diagonalization and CTQMC. We also perform full-fledged real-time calculations that have never been done before to our knowledge, which could be a benchmarking baseline for future method developments.

Quantum-Inspired Tensor-Network Fractional-Step Method for Incompressible Flow in Curvilinear Coordinates

Authors: Nis-Luca van Hülst, Pia Siegl, Paul Over, Sergio Bengoechea, Tomohiro Hashizume, Mario Guillaume Cecile, Thomas Rung, Dieter Jaksch

arXiv ID: 2507.05222 | Date: 2025-07-07

Abstract: We introduce an algorithmic framework based on tensor networks for computing fluid flows around immersed objects in curvilinear coordinates. We show that the tensor network simulations can be carried out solely using highly compressed tensor representations of the flow fields and the differential operators and discuss the numerical implementation of the tensor operations required for computing fluid flows in detail. The applicability of our method is demonstrated by applying it to the paradigm example of steady and transient flows around stationary and rotating cylinders. We find excellent quantitative agreement in comparison to finite difference simulations for Strouhal numbers, forces and velocity fields. The properties of our approach are discussed in terms of reduced order models. We estimate the memory saving and potential runtime advantages in comparison to standard finite difference simulations. We find accurate results with errors of less than 0.3% for flow-field compressions by a factor of up to 20 and differential operators compressed by factors of up to 1000 compared to sparse matrix representations. We provide strong numerical evidence that the runtime scaling advantages of the tensor network approach with system size will provide substantial resource savings when simulating larger systems. Finally, we note that, like other tensor network-based fluid flow simulations, our algorithmic framework is directly portable to a quantum computer leading to further scaling advantages.

An operator algebraic approach to fusion category symmetry on the lattice

Authors: David E. Evans, Corey Jones

arXiv ID: 2507.05185 | Date: 2025-07-07

Abstract: We propose a framework for fusion category symmetry on the (1+1)D lattice in the thermodynamic limit by giving a formal interpretation of SymTFT decompositions. Our approach is based on axiomatizing physical boundary subalgebra of quasi-local observables, and applying ideas from algebraic quantum field theory to derive the expected categorical structures. We show that given a physical boundary subalgebra BB of a quasi-local algebra AA, there is a canonical fusion category C\mathcal{C} that acts on AA by bimodules and whose fusion ring acts by locality preserving quantum channels on the quasi-local algebra such that BB is recovered as the fixed point operators. We show that a fusion category can be realized as symmetries on a tensor product quasi-local algebra if and only if all of its objects have integer dimensions, and that it admits an ``on-site" action on a tensor product spin chain if and only if it admits a fiber functor. We give a formal definition of a topological symmetric state, and prove two anomaly enforced gaplessness theorems, one for internal categorical symmetries and one for anomalous duality channels. Using the first, we show that for any fusion category C\mathcal{C} with no fiber functor there always exist gapless pure symmetric states on an anyon chain.

Instability of the Haldane Phase: Roles of Charge Fluctuations and Hund's Coupling

Authors: Satoshi Nishimoto

arXiv ID: 2507.05089 | Date: 2025-07-07

Abstract: We systematically investigate the stability of the symmetry-protected topological (SPT) Haldane phase in spin-1/2 Heisenberg and half-filled Hubbard ladders coupled by ferromagnetic Hund's interactions. Using density-matrix renormalization group (DMRG) method, we analyze key signatures of the Haldane phase: long-range string order, finite spin gap, and characteristic entanglement spectrum degeneracies. In spin-only Heisenberg ladders, we find immediate onset and continuous strengthening of the Haldane phase with increasing Hund's coupling. In contrast, the inclusion of charge fluctuations in Hubbard ladders leads to a nontrivial stability regime, revealing a robust yet bounded region where SPT order persists despite significant charge fluctuations. We identify distinct boundaries separating a trivial insulating phase from the Haldane SPT phase, governed by both Coulomb repulsion and Hund's coupling. Our results highlight the subtle interplay of spin and charge degrees of freedom in correlated itinerant systems and establish essential criteria for observing Haldane physics experimentally in fermionic ladder materials.

Disentangling strategies and entanglement transitions in unitary circuit games with matchgates

Authors: Raúl Morral-Yepes, Marc Langer, Adam Gammon-Smith, Barbara Kraus, Frank Pollmann

arXiv ID: 2507.05055 | Date: 2025-07-07

Abstract: In unitary circuit games, two competing parties, an "entangler" and a "disentangler", can induce an entanglement phase transition in a quantum many-body system. The transition occurs at a certain rate at which the disentangler acts. We analyze such games within the context of matchgate dynamics, which equivalently corresponds to evolutions of non-interacting fermions. We first investigate general entanglement properties of fermionic Gaussian states (FGS). We introduce a representation of FGS using a minimal matchgate circuit capable of preparing the state and derive an algorithm based on a generalized Yang-Baxter relation for updating this representation as unitary operations are applied. This representation enables us to define a natural disentangling procedure that reduces the number of gates in the circuit, thereby decreasing the entanglement contained in the system. We then explore different strategies to disentangle the systems and study the unitary circuit game in two different scenarios: with braiding gates, i.e., the intersection of Clifford gates and matchgates, and with generic matchgates. For each model, we observe qualitatively different entanglement transitions, which we characterize both numerically and analytically.

Moiré-assisted charge instability in ultrathin RuO2_2

Authors: Philipp Keßler, Andreas Feuerpfeil, Armando Consiglio, Hendrik Hohmann, Ronny Thomale, Jonas Erhardt, Bing Liu, Vedran Jovic, Ralph Claessen, Patrick Härtl, Matteo Dürrnagel, Simon Moser

arXiv ID: 2507.05047 | Date: 2025-07-07

Abstract: Ruthenium dioxide (RuO2_2) has been in the focus of contemporary condensed matter research as a prototypical candidate material for altermagnetism. In the face of daunting evidence for bulk magnetic order despite promising theoretical predictions, it naturally suggests the focus on thin films where Coulomb interactions are dimensionally quenched and may yield a more strongly correlated environment prone to magnetic ordering. Here, we combine scanning tunneling microscopy (STM), density functional theory (DFT), and density matrix renormalization group (DMRG) methods to investigate atomically ordered ultrathin RuO2_2(110) grown on Ru(0001). Contrary to predictions of magnetic order, we observe a nonmagnetic charge density wave (CDW) instability that is driven by Fermi surface nesting within the flat-band surface state, and stabilized by the incommensurate moiré stacking with the substrate. We further identify a nonmagnetic and metastable 2 ×\times 2 surface reconstruction that breaks in-plane mirror symmetry and can be reversibly toggled via STM tip manipulation. Our spin-polarized STM measurements find no sign of any magnetic instability at the RuO2_2 surface. As much as our findings refute proposals for either bulk or surface magnetism in RuO2_2, we establish ultrathin RuO2_2(110) as an intriguing platform for exploring Moiré-assisted electronic surface order.

Monte Carlo Tree Search with Tensor Factorization for Robot Optimization

Authors: Teng Xue, Yan Zhang, Amirreza Razmjoo, Sylvain Calinon

arXiv ID: 2507.04949 | Date: 2025-07-07

Abstract: Many robotic tasks, such as inverse kinematics, motion planning, and optimal control, can be formulated as optimization problems. Solving these problems involves addressing nonlinear kinematics, complex contact dynamics, long-horizon correlation, and multi-modal landscapes, each posing distinct challenges for state-of-the-art optimization methods. Monte Carlo Tree Search is a powerful approach that can strategically explore the solution space and can be applied to a wide range of tasks across varying scenarios. However, it typically suffers from combinatorial complexity when applied to robotics, resulting in slow convergence and high memory demands. To address this limitation, we propose \emph{Tensor Train Tree Search} (TTTS), which leverages tensor factorization to exploit correlations among decision variables arising from common kinematic structures, dynamic constraints, and environmental interactions in robot decision-making. This yields a compact, linear-complexity representation that significantly reduces both computation time and storage requirements. We prove that TTTS can efficiently reach the bounded global optimum within a finite time. Experimental results across inverse kinematics, motion planning around obstacles, legged robot manipulation, multi-stage motion planning, and bimanual whole-body manipulation demonstrate the efficiency of TTTS on a diverse set of robotic tasks.

Solving the Gross-Pitaevskii Equation with Quantic Tensor Trains: Ground States and Nonlinear Dynamics

Authors: Qian-Can Chen, I-Kang Liu, Jheng-Wei Li, Chia-Min Chung

arXiv ID: 2507.04279 | Date: 2025-07-06

Abstract: We develop a tensor network framework based on the quantic tensor train (QTT) format to efficiently solve the Gross-Pitaevskii equation (GPE), which governs Bose-Einstein condensates under mean-field theory. By adapting time-dependent variational principle (TDVP) and gradient descent methods, we accurately handle the GPE's nonlinearities within the QTT structure. Our approach enables high-resolution simulations with drastically reduced computational cost. We benchmark ground states and dynamics of BECs--including vortex lattice formation and breathing modes--demonstrating superior performance over conventional grid-based methods and stable long-time evolution due to saturating bond dimensions. This establishes QTT as a powerful tool for nonlinear quantum simulations.

Solving the Gross-Pitaevskii equation on multiple different scales using the quantics tensor train representation

Authors: Marcel Niedermeier, Adrien Moulinas, Thibaud Louvet, Jose L. Lado, Xavier Waintal

arXiv ID: 2507.04262 | Date: 2025-07-06

Abstract: Solving partial differential equations of highly featured problems represents a formidable challenge, where reaching high precision across multiple length scales can require a prohibitive amount of computer memory or computing time. However, the solutions to physics problems typically have structures operating on different length scales, and as a result exhibit a high degree of compressibility. Here, we use the quantics tensor train representation to build a solver for the time-dependent Gross-Pitaevskii equation. We demonstrate that the quantics approach generalizes well to the presence of the non-linear term in the equation. We show that we can resolve phenomena across length scales separated by seven orders of magnitude in one dimension within one hour on a single core in a laptop, greatly surpassing the capabilities of more naive methods. We illustrate our methodology with various modulated optical trap potentials presenting features at vastly different length scales, including solutions to the Gross-Pitaevskii equation on two-dimensional grids above a trillion points (220×2202^{20} \times 2^{20}). This quantum-inspired methodology can be readily extended to other partial differential equations combining spatial and temporal evolutions, providing a powerful method to solve highly featured differential equations at unprecedented length scales.

Independent Set Enumeration and Estimation of Related Constants of Grid Graphs and Their Variants

Authors: Kai Liang

arXiv ID: 2507.04007 | Date: 2025-07-05

Abstract: We applied tensor network contraction algorithms to compute the hard-core lattice gas model, i.e., the enumeration of independent sets on grid graphs. We observed the influence of surface effect and parity effect on the enumeration (and entropy), and derived upper and lower bounds for both the combinatorics entropy and the coefficients of surface effect by numerical analysis. Additionally, we conducted corresponding calculations and analyses for triangular grid graphs, king graph, and cylindrical grid graph. We computed and analyzed their associated constants and compared how different adjacency and boundary conditions affect these constants. Our computational results have contributed substantial new terms to the OEIS sequence A089980, A027740, A219741, A226444, A245013 and A286513. In addition, we have provided fairly accurate estimates of the relevant constants through numerical analysis of the obtained results. Among them, our valuation of the hard square entropy constant is more accurate than existing results. And we conject that the surface effect of the periodic boundary of the cylindrical grid graph is 00--its estimated value of coefficients is very close to 00.

Entanglement transitions in structured and random nonunitary Gaussian circuits

Authors: Bastien Lapierre, Liang-Hong Mo, Shinsei Ryu

arXiv ID: 2507.03768 | Date: 2025-07-04

Abstract: We study measurement-induced phase transitions in quantum circuits consisting of kicked Ising models with postselected weak measurements, whose dynamics can be mapped onto a classical dynamical system. For a periodic (Floquet) non-unitary evolution, such circuits are exactly tractable and admit volume-to-area law transitions. We show that breaking time-translation symmetry down to a quasiperiodic (Fibonacci) time evolution leads to the emergence of a critical phase with tunable effective central charge and with a fractal origin. Furthermore, for some classes of random non-unitary circuits, we demonstrate the robustness of the volume-to-area law phase transition for arbitrary random realizations, thanks to the emergent compactness of the classical map encoding the circuit's dynamics.

Quantics Tensor Train for solving Gross-Pitaevskii equation

Authors: Aleix Bou-Comas, Marcin Płodzień, Luca Tagliacozzo, Juan José García-Ripoll

arXiv ID: 2507.03134 | Date: 2025-07-03

Abstract: We present a quantum-inspired solver for the one-dimensional Gross-Pitaevskii equation in the Quantics Tensor-Train (QTT) representation. By evolving the system entirely within a low-rank tensor manifold, the method sidesteps the memory and runtime barriers that limit conventional finite-difference and spectral schemes. Two complementary algorithms are developed: an imaginary-time projector that drives the condensate toward its variational ground state and a rank-adapted fourth-order Runge-Kutta integrator for real-time dynamics. The framework captures a broad range of physical scenarios - including barrier-confined condensates, quasi-random potentials, long-range dipolar interactions, and multicomponent spinor dynamics - without leaving the compressed representation. Relative to standard discretizations, the QTT approach achieves an exponential reduction in computational resources while retaining quantitative accuracy, thereby extending the practicable regime of Gross-Pitaevskii simulations on classical hardware. These results position tensor networks as a practical bridge between high-performance classical computing and prospective quantum hardware for the numerical treatment of nonlinear Schrodinger-type partial differential equations.

Dynamical correlation functions for the one-dimensional Bose-Hubbard insulator

Authors: Kevin zu Münster, Florian Gebhard, Satoshi Ejima, Holger Fehske

arXiv ID: 2507.03125 | Date: 2025-07-03

Abstract: We calculate the dynamical current and kinetic-energy correlation functions for the first Mott lobe of the one-dimensional Bose-Hubbard model. We employ the strong-coupling expansion up to sixth order in x=t/Ux=t/U, and the dynamical density-matrix renormalization group method on rings with 64 sites. The correlation functions are finite above the single-particle gap with a square-root onset, as is also found from field theory close to the Mott transition. The correlation functions display a featureless superposition of the primary and tertiary Hubbard bands. We find very good agreement between all methods in the interaction/frequency regimes where they are applicable.

Imprints of information scrambling on eigenstates of a quantum chaotic system

Authors: Bikram Pain, Ratul Thakur, Sthitadhi Roy

arXiv ID: 2507.02853 | Date: 2025-07-03

Abstract: How are the spatial and temporal patterns of information scrambling in locally interacting quantum many-body systems imprinted on the eigenstates of the system's time-evolution operator? We address this question by identifying statistical correlations among sets of minimally four eigenstates that provide a unified framework for various measures of information scrambling. These include operator mutual information and operator entanglement entropy of the time-evolution operator, as well as more conventional diagnostics such as two-point dynamical correlations and out-of-time-ordered correlators. We demonstrate this framework by deriving exact results for eigenstate correlations in a minimal model of quantum chaos -- Floquet dual-unitary circuits. These results reveal not only the butterfly effect and the information lightcone, but also finer structures of scrambling within the lightcone. Our work thus shows how the eigenstates of a chaotic system can encode the full spatiotemporal anatomy of quantum chaos, going beyond the descriptions offered by random matrix theory and the eigenstate thermalisation hypothesis.

The covariance matrix spectrum of correlated charge insulators reveals hidden connections to Coupled Cluster, Matrix Product, and Rokhsar-Kivelson states

Authors: Izak Snyman, Serge Florens

arXiv ID: 2507.02625 | Date: 2025-07-03

Abstract: Charge ordering induced by strong short-range repulsion in itinerant fermion systems typically follows a two-sites alternation pattern. However, the covariance matrix spectrum of the one-dimensional, half-filled, spinless tt-VV model reveals a post-Hartree-Fock picture at strong repulsion, with emergent four-site disruptions of the underlying staggered mean-field state. These disruptions are captured in a thermodynamically extensive manner by a compact four-fermion Coupled Cluster (doubles) state (CCS). Remarkably, all properties of this state may be computed analytically by combinatorial means, and also derived from an exactly solvable correlated hopping Hamiltonian. Furthermore, this Coupled Cluster state can be re-expressed as a low-rank Matrix Product State (MPS) with bond dimension exactly four. In addition, we unveil a hidden connection between this Coupled Cluster ansatz and a Rokhsar-Kivelson state (RKS), which is the ground state of a solvable parent quantum tetramer model. The broad picture that we uncover here thus provides deep connections between several core concepts of correlated fermions and quantum chemistry that have previously enjoyed limited synergy. In contrast to a recent perturbative treatment on top of Hartree-Fock theory, our approach asymptotically captures the correct correlations in the tt-VV model at small t/Vt/V, and remains a qualitatively accurate approximation even outside the perturbative regime. Our results make the case for further studies of the covariance matrix for correlated electron systems in which ground states have non-trivial unit-cell structure.

Hall-on-Toric: Descendant Laughlin state in the chiral Zp\mathbb{Z}_p toric code

Authors: Robin Schäfer, Claudio Chamon, Chris R. Laumann

arXiv ID: 2507.02035 | Date: 2025-07-02

Abstract: We demonstrate that the chiral Zp\mathbb{Z}_p toric code -- the quintessential model of topological order -- hosts additional, emergent topological phases when perturbed: descendant fractional quantum Hall-like states, which we term \textit{Hall-on-Toric}. These hierarchical states feature fractionalized Zp\mathbb{Z}_p charges and increased topological ground-state degeneracy. The Hall-on-Toric phases appear in the vicinity of the transitions between deconfined Zp\mathbb{Z}_p phases with different background charge per unit cell, in a fixed non-trivial flux background. We confirm their existence through extensive infinite density matrix renormalization group (iDMRG) simulations, analyzing the topological entanglement entropy, entanglement spectra, and a generalized Hall conductance. Remarkably, the Hall-on-Toric states remain robust even in the absence of U(1)U(1) symmetry. Our findings reinforce the foundational interpretation of star and plaquette defects as magnetic and electric excitations, and reveal that this perspective extends to a much deeper level.

String Breaking Dynamics and Glueball Formation in a 2+12+1D Lattice Gauge Theory

Authors: Kaidi Xu, Umberto Borla, Sergej Moroz, Jad C. Halimeh

arXiv ID: 2507.01950 | Date: 2025-07-02

Abstract: With the advent of advanced quantum processors capable of probing lattice gauge theories (LGTs) in higher spatial dimensions, it is crucial to understand string dynamics in such models to guide upcoming experiments and to make connections to high-energy physics (HEP). Using tensor network methods, we study the far-from-equilibrium quench dynamics of electric flux strings between two static charges in the 2+12+1D Z2\mathbb{Z}_2 LGT with dynamical matter. We calculate the probabilities of finding the time-evolved wave function in string configurations of the same length as the initial string. At resonances determined by the the electric field strength and the mass, we identify various string breaking processes accompanied with matter creation. Away from resonance strings exhibit intriguing confined dynamics which, for strong electric fields, we fully characterize through effective perturbative models. Starting in maximal-length strings, we find that the wave function enters a dynamical regime where it splits into shorter strings and disconnected loops, with the latter bearing qualitative resemblance to glueballs in quantum chromodynamics (QCD). Our findings can be probed on state-of-the-art superconducting-qubit and trapped-ion quantum processors.

Quantum Machine Learning in Transportation: A Case Study of Pedestrian Stress Modelling

Authors: Bara Rababah, Bilal Farooq

arXiv ID: 2507.01235 | Date: 2025-07-01

Abstract: Quantum computing has opened new opportunities to tackle complex machine learning tasks, for instance, high-dimensional data representations commonly required in intelligent transportation systems. We explore quantum machine learning to model complex skin conductance response (SCR) events that reflect pedestrian stress in a virtual reality road crossing experiment. For this purpose, Quantum Support Vector Machine (QSVM) with an eight-qubit ZZ feature map and a Quantum Neural Network (QNN) using a Tree Tensor Network ansatz and an eight-qubit ZZ feature map, were developed on Pennylane. The dataset consists of SCR measurements along with features such as the response amplitude and elapsed time, which have been categorized into amplitude-based classes. The QSVM achieved good training accuracy, but had an overfitting problem, showing a low test accuracy of 45% and therefore impacting the reliability of the classification model. The QNN model reached a higher test accuracy of 55%, making it a better classification model than the QSVM and the classic versions.

Tensor network methods for the Gross-Pitaevskii equation on fine grids

Authors: Ryan J. J. Connor, Callum W. Duncan, Andrew J. Daley

arXiv ID: 2507.01149 | Date: 2025-07-01

Abstract: The Gross-Pitaevskii equation and its generalisations to dissipative and dipolar gases have been very useful in describing dynamics of cold atomic gases, as well as polaritons and other nonlinear systems. For some of these applications the numerically accessible grid spacing can become a limiting factor, especially in describing turbulent dynamics and short-range effects of dipole-dipole interactions. We explore the application of tensor networks to these systems, where (in analogy to related work in fluid and plasma dynamics), they allow for physically motivated data compression that makes simulations possible on large spatial grids which would be unfeasible with direct numerical simulations. Analysing different non-equilibrium cases involving vortex formation, we find that these methods are particularly efficient, especially in combination with a matrix product operator representation of the quantum Fourier transform, which enables a spectral approach to calculation of both equilibrium states and time-dependent dynamics. The efficiency of these methods has interesting physical implications for the structure in the states that are generated by these dynamics, and provides a path to describe cold gas experiments that are challenging for existing methods.

Charge pumps, pivot Hamiltonians and symmetry-protected topological phases

Authors: Nick. G. Jones, Ryan Thorngren, Ruben Verresen, Abhishodh Prakash

arXiv ID: 2507.00995 | Date: 2025-07-01

Abstract: Generalised charge pumps are topological obstructions to trivialising loops in the space of symmetric gapped Hamiltonians. We show that given mild conditions on such pumps, the associated loop has high-symmetry points which must be in distinct symmetry-protected topological (SPT) phases. To further elucidate the connection between pumps and SPTs, we focus on closed paths, `pivot loops', defined by two Hamiltonians, where the first is unitarily evolved by the second `pivot' Hamiltonian. While such pivot loops have been studied as entanglers for SPTs, here we explore their connection to pumps. We construct families of pivot loops which pump charge for various symmetry groups, often leading to SPT phases -- including dipole SPTs. Intriguingly, we find examples where non-trivial pumps do not lead to genuine SPTs but still entangle representation-SPTs (RSPTs). We use the anomaly associated to the non-trivial pump to explain the a priori `unnecessary' criticality between these RSPTs. We also find that particularly nice pivot families form circles in Hamiltonian space, which we show is equivalent to the Hamiltonians satisfying the Dolan-Grady relation -- known from the study of integrable models. This additional structure allows us to derive more powerful constraints on the phase diagram. Natural examples of such circular loops arise from pivoting with the Onsager-integrable chiral clock models, containing the aforementioned RSPT example. In fact, we show that these Onsager pivots underlie general group cohomology-based pumps in one spatial dimension. Finally, we recast the above in the language of equivariant families of Hamiltonians and relate the invariants of the pump to the candidate SPTs. We also highlight how certain SPTs arise in cases where the equivariant family is labelled by spaces that are not manifolds.

Complete Boundary Phase Diagram of the Spin-12\frac{1}{2} XXZ Chain with Boundary Fields in the Anti-Ferromagnetic Gapped Regime

Authors: Parameshwar R. Pasnoori, Yicheng Tang, Junhyun Lee, J. H. Pixley, Patrick Azaria, Natan Andrei

arXiv ID: 2507.00386 | Date: 2025-07-01

Abstract: We consider the spin 12\frac{1}{2} XXZ chain with diagonal boundary fields and solve it exactly using Bethe ansatz in the gapped anti-ferromagnetic regime and obtain the complete phase boundary diagram. Depending on the values of the boundary fields, the system exhibits several phases which can be categorized based on the ground state exhibited by the system and also based on the number of bound states localized at the boundaries. We show that the Hilbert space is comprised of a certain number of towers whose number depends on the number of boundary bound states exhibited by the system. The system undergoes boundary phase transitions when boundary fields are varied across certain critical values. There exist two types of phase transitions. In the first type the ground state of the system undergoes a change. In the second type, named the `Eigenstate phase transition', the number of towers of the Hilbert space changes, which is again associated with the change in the number of boundary bound states exhibited by the system. We use the DMRG and exact diagonalization techniques to probe the signature of the Eigenstate phase transition and the ground state phase transition by analyzing the spin profiles in each eigenstate.

Multi-Target Density Matrix Renormalization Group X algorithm and its application to circuit quantum electrodynamics

Authors: Sofía González-García, Aaron Szasz, Alice Pagano, Dvir Kafri, Guifré Vidal, Agustin Di Paolo

arXiv ID: 2506.24109 | Date: 2025-06-30

Abstract: Obtaining accurate representations of the eigenstates of an array of coupled superconducting qubits is a crucial step in the design of circuit quantum electrodynamics (QED)-based quantum processors. However, exact diagonalization of the device Hamiltonian is challenging for system sizes beyond tens of qubits. Here, we employ a variant of the density matrix renormalization group (DMRG) algorithm, DMRG-X, to efficiently obtain localized eigenstates of a 2D transmon array without the need to first compute lower-energy states. We also introduce MTDMRG-X, a new algorithm that combines DMRG-X with multi-target DMRG to efficiently compute excited states even in regimes with strong eigenstate hybridization. We showcase the use of these methods for the analysis of long-range couplings in a multi-transmon Hamiltonian including qubits and couplers, and we discuss eigenstate localization. These developments facilitate the design and parameter optimization of large-scale superconducting quantum processors.

Ruelle-Pollicott resonances of diffusive U(1)-invariant qubit circuits

Authors: Urban Duh, Marko Žnidarič

arXiv ID: 2506.24097 | Date: 2025-06-30

Abstract: We study Ruelle-Pollicott resonances of translationally invariant magnetization-conserving qubit circuits via the spectrum of the quasi-momentum-resolved truncated propagator of extensive observables. Diffusive transport of the conserved magnetization is reflected in the Gaussian quasi-momentum kk dependence of the leading eigenvalue (Ruelle-Pollicott resonance) of the truncated propagator for small kk. This, in particular, allows us to extract the diffusion constant. For large kk, the leading Ruelle-Pollicott resonance is not related to transport and governs the exponential decay of correlation functions. Additionally, we conjecture the existence of a continuum of eigenvalues below the leading diffusive resonance, which governs non-exponential decay, for instance, power-law hydrodynamic tails. We expect our conclusions to hold for generic systems with exactly one U(1) conserved quantity.

Canonical partial ordering from min-cuts and quantum entanglement in random tensor networks

Authors: Miao Hu, Ion Nechita

arXiv ID: 2506.23894 | Date: 2025-06-30

Abstract: The \emph{max-flow min-cut theorem} has been recently used in the theory of random tensor networks in quantum information theory, where it is helpful for computing the behavior of important physical quantities, such as the entanglement entropy. In this paper, we extend the max-flow min-cut theorem to a relation among different \emph{partial orders} on the set of vertices of a network and introduce a new partial order for the vertices based on the \emph{min-cut structure} of the network. We apply the extended max-flow min-cut theorem to random tensor networks and find that the \emph{finite correction} to the entanglement Rényi entropy arising from the degeneracy of the min-cuts is given by the number of \emph{order morphisms} from the min-cut partial order to the partial order induced by non-crossing partitions on the symmetric group. Moreover, we show that the number of order morphisms corresponds to moments of a graph-dependent measure which generalizes the free Bessel law in some special cases in free probability theory.

High-Performance Contraction of Quantum Circuits for Riemannian Optimization

Authors: Fabian Putterer, Max M. Zumpe, Isabel Nha Minh Le, Qunsheng Huang, Christian B. Mendl

arXiv ID: 2506.23775 | Date: 2025-06-30

Abstract: This work focuses on optimizing the gates of a quantum circuit with a given topology to approximate the unitary time evolution governed by a Hamiltonian. Recognizing that unitary matrices form a mathematical manifold, we employ Riemannian optimization methods -- specifically the Riemannian trust-region algorithm -- which involves second derivative calculations with respect to the gates. Our key technical contribution is a matrix-free algorithmic framework that avoids the explicit construction and storage of large unitary matrices acting on the whole Hilbert space. Instead, we evaluate all quantities as sums over state vectors, assuming that these vectors can be stored in memory. We develop HPC-optimized kernels for applying gates to state vectors and for the gradient and Hessian computation. Further improvements are achieved by exploiting sparsity structures due to Hamiltonian conservation laws, such as parity conservation, and lattice translation invariance. We benchmark our implementation on the Fermi-Hubbard model with up to 16 sites, demonstrating a nearly linear parallelization speed-up with up to 112 CPU threads. Finally, we compare our implementation with an alternative matrix product operator-based approach.

Tensor Train Quantum State Tomography using Compressed Sensing

Authors: Shakir Showkat Sofi, Charlotte Vermeylen, Lieven De Lathauwer

arXiv ID: 2506.23560 | Date: 2025-06-30

Abstract: Quantum state tomography (QST) is a fundamental technique for estimating the state of a quantum system from measured data and plays a crucial role in evaluating the performance of quantum devices. However, standard estimation methods become impractical due to the exponential growth of parameters in the state representation. In this work, we address this challenge by parameterizing the state using a low-rank block tensor train decomposition and demonstrate that our approach is both memory- and computationally efficient. This framework applies to a broad class of quantum states that can be well approximated by low-rank decompositions, including pure states, nearly pure states, and ground states of Hamiltonians.

Seeding neural network quantum states with tensor network states

Authors: Ryui Kaneko, Shimpei Goto

arXiv ID: 2506.23550 | Date: 2025-06-30

Abstract: We find an efficient approach to approximately convert matrix product states (MPSs) into restricted Boltzmann machine wave functions consisting of a multinomial hidden unit through a canonical polyadic (CP) decomposition of the MPSs. This method allows us to generate well-behaved initial neural network quantum states for quantum many-body ground-state calculations in polynomial time of the number of variational parameters and systematically shorten the distance between the initial states and the ground states while increasing the rank of the CP decomposition. We demonstrate the efficiency of our method by taking the transverse-field Ising model as an example and discuss possible applications of our method to more general quantum many-body systems in which the ground-state wave functions possess complex nodal structures.

Extended Non-Markovian Stochastic Schrödinger Equation with Complex Frequency Modes for General Basis Functions

Authors: Yukai Guo, Zeyu Huang, Xing Gao

arXiv ID: 2506.22738 | Date: 2025-06-28

Abstract: We introduce an extended formulation of the non-Markovian stochastic Schrödinger equation with complex frequency modes (extended cNMSSE), designed for simulating open quantum system dynamics under arbitrary spectral densities. This extension employs non-exponential basis sets to expand the bath correlation functions, overcoming the reliance of the original cNMSSE on exponential decompositions of the spectral density. Consequently, the extended cNMSSE is applicable to environments beyond those characterized by Debye-type spectral densities. The flexibility to employ general basis functions is particularly advantageous for handling spectral densities with higher-order poles, for which exponential decompositions are often inaccurate or unavailable. The extended cNMSSE is implemented in a pseudo-Fock space using conventional ladder operators and solved efficiently via matrix product state (MPS) techniques, preserving the favorable linear-scaling and wavefunction-based nature of the original method. Benchmark simulations across four representative cases, including discrete spectral density, Ohmic spectral density with exponential and algebraic cutoffs, and critically damped Brownian spectral density, demonstrate excellent agreement with results of hierarchy of forward-backward stochastic Schrödinger equations (HFB-SSE) and extended hierarchical equation of motion (HEOM).

Computing excited eigenstates using inexact Lanczos methods and tree tensor network states

Authors: Madhumita Rano, Henrik R. Larsson

arXiv ID: 2506.22574 | Date: 2025-06-27

Abstract: To understand the dynamics of quantum many-body systems, it is essential to study excited eigenstates. While tensor network states have become a standard tool for computing ground states in computational many-body physics, obtaining accurate excited eigenstates remains a significant challenge. In this work, we develop an approach that combines the inexact Lanczos method, which is designed for efficient computations of excited states, with tree tensor network states (TTNSs). We demonstrate our approach by computing excited vibrational states for three challenging problems: (1) 122 states in two different energy intervals of acetonitrile (12-dimensional), (2) Fermi resonance states of the fluxional Zundel ion (15-dimensional), and (3) selected excited states of the fluxional and very correlated Eigen ion (33-dimensional). The proposed TTNS inexact Lanczos method is directly applicable to other quantum many-body systems.

Conformal scalar field theory from Ising tricriticality on the fuzzy sphere

Authors: Joseph Taylor, Cristian Voinea, Zlatko Papić, Ruihua Fan

arXiv ID: 2506.22539 | Date: 2025-06-27

Abstract: Free theories are landmarks in the landscape of quantum field theories: their exact solvability serves as a pillar for perturbative constructions of interacting theories. Fuzzy sphere regularization, which combines quantum Hall physics with state-operator correspondence, has recently been proposed as a promising framework for simulating three-dimensional conformal field theories (CFTs), but so far it has not provided access to free theories. We overcome this limitation by designing a bilayer quantum Hall system that hosts an Ising tricritical point -- a nontrivial fixed point where first-order and second-order transitions meet -- which flows to the conformally coupled scalar theory in the infrared. The critical energy spectrum and operator structure match those at the Gaussian fixed point, providing nonperturbative evidence for the emergence of a free scalar CFT. Our results expand the landscape of CFTs realizable on the fuzzy sphere and demonstrate that even free bosonic theories -- previously inaccessible -- can emerge from interacting electrons in this framework.

Spin Seebeck Effect of Triangular-lattice Spin Supersolid

Authors: Yuan Gao, Yixuan Huang, Sadamichi Maekawa, Wei Li

arXiv ID: 2506.22414 | Date: 2025-06-27

Abstract: Using thermal tensor-network approach, we investigate the spin Seebeck effect (SSE) of the triangular-lattice quantum antiferromagnet hosting spin supersolid phase. We focus on the low-temperature scaling behaviors of the normalized spin current across the interface. For the 1D Heisenberg chain, we find a negative spinon spin in the bulk current with algebraic temperature scaling; at low fields, boundary effects induce a second sign reversal at lower temperatures. These benchmark results are consistent with field-theoretical analysis. On the triangular lattice, spin frustration dramatically enhances the low-temperature SSE, with distinct spin-current signatures -- particularly the sign reversal and characteristic temperature dependence -- distinguishing different spin states. Remarkably, we discover a persistent, negative spin current in the spin supersolid phase, which saturates to a non-zero value in the low-temperature limit and can be ascribed to the Goldstone-mode-mediated spin supercurrents. Moreover, a universal scaling Td/zT^{d/z} is found at the U(1)-symmetric polarization quantum critical points. These distinct quantum spin transport traits provide sensitive spin current probes for spin supersolid states in quantum magnets such as Na2_2BaCo(PO4_4)2_2. Furthermore, our results also establish spin supersolids as a tunable quantum platform for spin caloritronics in the ultralow-temperature regime.

Causal Decompositions of 1D Quantum Cellular Automata

Authors: Augustin Vanrietvelde, Octave Mestoudjian, Pablo Arrighi

arXiv ID: 2506.22219 | Date: 2025-06-27

Abstract: Understanding quantum theory's causal structure stands out as a major matter, since it radically departs from classical notions of causality. We present advances in the research program of causal decompositions, which investigates the existence of an equivalence between the causal and the compositional structures of unitary channels. Our results concern one-dimensional Quantum Cellular Automata (1D QCAs), i.e. unitary channels over a line of NN quantum systems (with or without periodic boundary conditions) that feature a causality radius rr: a given input cannot causally influence outputs at a distance more than rr. We prove that, for N4r+1N \geq 4r + 1, 1D QCAs all admit causal decompositions: a unitary channel is a 1D QCA if and only if it can be decomposed into a unitary routed circuit of nearest-neighbour interactions, in which its causal structure is compositionally obvious. This provides the first constructive form of 1D QCAs with causality radius one or more, fully elucidating their structure. In addition, we show that this decomposition can be taken to be translation-invariant for the case of translation-invariant QCAs. Our proof of these results makes use of innovative algebraic techniques, leveraging a new framework for capturing partitions into non-factor sub-C* algebras.

Low-Rank Tensor Recovery via Variational Schatten-p Quasi-Norm and Jacobian Regularization

Authors: Zhengyun Cheng, Ruizhe Zhang, Guanwen Zhang, Yi Xu, Xiangyang Ji, Wei Zhou

arXiv ID: 2506.22134 | Date: 2025-06-27

Abstract: Higher-order tensors are well-suited for representing multi-dimensional data, such as images and videos, which typically characterize low-rank structures. Low-rank tensor decomposition has become essential in machine learning and computer vision, but existing methods like Tucker decomposition offer flexibility at the expense of interpretability. The CANDECOMP/PARAFAC (CP) decomposition provides a natural and interpretable structure, while obtaining a sparse solutions remains challenging. Leveraging the rich properties of CP decomposition, we propose a CP-based low-rank tensor function parameterized by neural networks (NN) for implicit neural representation. This approach can model the tensor both on-grid and beyond grid, fully utilizing the non-linearity of NN with theoretical guarantees on excess risk bounds. To achieve sparser CP decomposition, we introduce a variational Schatten-p quasi-norm to prune redundant rank-1 components and prove that it serves as a common upper bound for the Schatten-p quasi-norms of arbitrary unfolding matrices. For smoothness, we propose a regularization term based on the spectral norm of the Jacobian and Hutchinson's trace estimator. The proposed smoothness regularization is SVD-free and avoids explicit chain rule derivations. It can serve as an alternative to Total Variation (TV) regularization in image denoising tasks and is naturally applicable to implicit neural representation. Extensive experiments on multi-dimensional data recovery tasks, including image inpainting, denoising, and point cloud upsampling, demonstrate the superiority and versatility of our method compared to state-of-the-art approaches. The code is available at https://github.com/CZY-Code/CP-Pruner.

Dipoles and Anyonic Directional Confinement via Twisted Toric Codes

Authors: Jose Garre Rubio

arXiv ID: 2506.22025 | Date: 2025-06-27

Abstract: We introduce a modified 2D toric code Hamiltonian that exhibits explicit anyon confinement along a single spatial direction. By bounding the motion of these confined anyons, we obtain dipolar excitations with restricted mobility. We analyze the resulting logical operators, whose existence depends on the system size, as well as the structure of gapped boundaries and a tensor network representation of the ground state. Furthermore, when confinement is enforced in both directions, fractal-like excitations emerge, resulting in unpaired logical operators. We extend our construction to 3D models, such as the surface code and the X-cube model, leading to novel dipole-loop and dipole-planon excitations that arise from bounding confined excitations. These modifications are implemented through group cohomological twistings--projective representations of finite groups--with most examples based on Z2xZ2.

Resonating Kagome Dimer coverings in Rydberg atom arrays

Authors: Xicheng Wang, Erich J Mueller

arXiv ID: 2506.21255 | Date: 2025-06-26

Abstract: Motivated by experiments on Rydberg atom arrays, we explore the properties of uniform quantum superpositions of kagome dimer configurations and construct an efficient algorithm for experimentally producing them. We begin by considering the thin cylinder limit, where these states have simple descriptions. We then develop a matrix product representation of the states on arbitrary cylinders, which leads to a natural protocol to efficiently grow them. We explain how our approach can be adapted to other quantum computing hardware.

A Survey on Continuous Variable Quantum Key Distribution for Secure Data Transmission: Toward the Future of Secured Quantum-Networks

Authors: Mobin Motaharifar, Mahmood Hasani, Hassan Kaatuzian

arXiv ID: 2506.21640 | Date: 2025-06-25

Abstract: Quantum key distribution (QKD) represents a cornerstone of secure communication in the quantum era. While discrete-variable QKD (DV-QKD) protocols were historically the first to demonstrate secure key exchange, continuous-variable QKD (CV-QKD) has emerged as a more practical alternative due to its seamless compatibility with current telecommunications infrastructure. CV-QKD relies on coherent and squeezed states of light, offering significant advantages for integration into modern optical networks. This review comprehensively explores the theoretical underpinnings, technological advancements, and practical challenges of CV-QKD. Special attention is given to the role of photonic integrated circuits (PICs) in enabling scalable and efficient implementation of CV-QKD systems. Furthermore, recent advances in machine learning have been leveraged to optimize CV-QKD performance, with data-driven techniques enhancing noise estimation, parameter optimization, and system security. Additionally, tensor networks provide efficient computational tools for analyzing complex quantum correlations, improving the efficiency and robustness of quantum key distribution protocols. These developments, combined with ongoing improvements in quantum photonic integration, pave the way for the practical deployment of large-scale, high-speed quantum-secure networks.

Quantum Utility-Scale Error Mitigation for Quantum Quench Dynamics in Heisenberg Spin Chains

Authors: Seokwon Choi, Talal Ahmed Chowdhury, Kwangmin Yu

arXiv ID: 2506.20125 | Date: 2025-06-25

Abstract: We propose a quantum error mitigation method termed self-mitigation, which is comparable with zero-noise extrapolation, to achieve quantum utility on near-term, noisy quantum computers. We investigate the effectiveness of several quantum error mitigation strategies, including self-mitigation, by simulating quantum quench dynamics for Heisenberg spin chains with system sizes up to 104 qubits using IBM quantum processors. In particular, we discuss the limitations of zero-noise extrapolation and the advantages offered by self-mitigation at a large scale. The self-mitigation method shows stable accuracy with the large systems of 104 qubits with more than 3,000 CNOT gates. Also, we combine the discussed quantum error mitigation methods with practical entanglement entropy measuring methods, and it shows a good agreement with the theoretical estimation. Our study illustrates the usefulness of near-term noisy quantum hardware in examining the quantum quench dynamics of many-body systems at large scales, and lays the groundwork for surpassing classical simulations with quantum methods prior to the development of fault-tolerant quantum computers.

Algorithms for variational Monte Carlo calculations of fermion projected entangled pair states in the swap gates formulation and the detailed balance of tensor network sequential sampling

Authors: Yantao Wu, Zhehao Dai

arXiv ID: 2506.20106 | Date: 2025-06-25

Abstract: In recent years, the variational Monte Carlo (VMC) calculations of projected entangled pair states (PEPS) has emerged as a competitive method for computing the ground states of many-body quantum systems. This method is particularly important for fermion systems where sign problems are abundant. We derive and explain the algorithms for the VMC calculations of fermion PEPS in the swap gates formulation. As a separate key result, we prove the detailed balance of sequential sampling of tensor networks.

Holography for bulk-boundary local topological order

Authors: Corey Jones, Pieter Naaijkens, David Penneys

arXiv ID: 2506.19969 | Date: 2025-06-24

Abstract: In our previous article [arXiv:2307.12552], we introduced local topological order (LTO) axioms for quantum spin systems which allowed us to define a physical boundary manifested by a net of boundary algebras in one dimension lower. This gives a formal setting for topological holography, where the braided tensor category of DHR bimodules of the physical boundary algebra captures the bulk topological order. In this article, we extend the LTO axioms to quantum spin systems equipped with a topological boundary, again producing a physical boundary algebra for the bulk-boundary system, whose category of (topological) boundary DHR bimodules recovers the topological boundary order. We perform this analysis in explicit detail for Levin-Wen and Walker-Wang bulk-boundary systems. Along the way, we introduce a 2D braided categorical net of algebras built from a unitary braided fusion category (UBFC). Such nets arise as boundary algebras of Walker-Wang models. We consider the canonical state on this braided categorical net corresponding to the standard topological boundary for the Walker-Wang model. Interestingly, in this state, the cone von Neumann algebras are type I with finite dimensional centers, in contrast with the type II and III cone von Neumann algebras from the Levin-Wen models studied in [arXiv:2307.12552]. Their superselection sectors recover the underlying unitary category of our UBFC, and we conjecture the superselection category also captures the fusion and braiding.

Weak unitary symmetries of open quantum dynamics: beyond quantum master equations

Authors: Calum A. Brown, Robert L. Jack, Katarzyna Macieszczak

arXiv ID: 2506.19814 | Date: 2025-06-24

Abstract: We consider Markovian open quantum dynamics with weak unitary symmetries. Starting from the quantum master equation for the system alone, it is known that the joint dynamics of the system and its environment can be obtained by dilation, leading to a closed dynamics for a continuous matrix product state. Performing counting measurements on the environment gives rise to stochastic dynamics of quantum trajectories for the system, which when averaged yield back the quantum master equation. In this work, we identify necessary and sufficient conditions under which the dynamics of these different descriptions retain the weak symmetry of the quantum master equation and we characterise the resulting symmetries of the different descriptions in terms of their generators. We find that the joint dynamics always features a separable symmetry directly related to that of the quantum master equation, but for quantum trajectories the corresponding symmetry is present only if the counting measurement satisfies certain conditions.

Entanglement and quench dynamics in the thermally perturbed tricritical fixed point

Authors: Csilla Király, Máté Lencsés

arXiv ID: 2506.19596 | Date: 2025-06-24

Abstract: We consider the Blume--Capel model in the scaling limit to realize the thermal perturbation of the tricritical Ising fixed point. We develop a numerical scaling limit extrapolation for one-point functions and Rényi entropies in the ground state. In a mass quench scenario, we found long-lived oscillations despite the absence of explicit spin-flip symmetry breaking or confining potential. We construct form factors of branch-point twist fields in the paramagnetic phase. In the scaling limit of small quenches, we verify form factor predictions for the energy density and leading magnetic field using the dynamics of one-point functions, and branch-point twist fields using the dynamics of Rényi entropies.

Efficient optimization of variational tensor-network approach to three-dimensional statistical systems

Authors: Xia-Ze Xu, Tong-Yu Lin, Guang-Ming Zhang

arXiv ID: 2506.19339 | Date: 2025-06-24

Abstract: Variational tensor network optimization has become a powerful tool for studying classical statistical models in two dimensions. However, its application to three-dimensional systems remains limited, primarily due to the high computational cost associated with evaluating the free energy density and its gradient. This process requires contracting a triple-layer tensor network composed of a projected entangled pair operator and projected entangled pair states. In this paper, we employ a split corner-transfer renormalization group scheme tailored for the contraction of such a triple-layer network, which reduces the computational complexity while keeping high accuracy. Through numerical benchmarks on the three-dimensional classical Ising model, we demonstrate that the proposed scheme achieves numerical results comparable to the most recent Monte Carlo simulations, providing a substantial speedup over previous variational tensor network approaches. This makes this method well-suited for efficient gradient-based optimization in three-dimensional tensor network simulations.

Topological crystals and soliton lattices in a Gross-Neveu model with Hilbert-space fragmentation

Authors: Sergio Cerezo-Roquebrún, Simon Hands, Alejandro Bermudez

arXiv ID: 2506.18675 | Date: 2025-06-23

Abstract: We explore the finite-density phase diagram of the single-flavour Gross-Neveu-Wilson (GNW) model using matrix product state (MPS) simulations. At zero temperature and along the symmetry line of the phase diagram, we find a sequence of inhomogeneous ground states that arise through a real-space version of the mechanism of Hilbert-space fragmentation. For weak interactions, doping the symmetry-protected topological (SPT) phase of the GNW model leads to localized charges or holes at periodic arrangements of immobile topological defects separating the fragmented subchains: a topological crystal. Increasing the interactions, we observe a transition into a parity-broken phase with a pseudoscalar condensate displaying a modulated periodic pattern. This soliton lattice is a sequence of topological charges corresponding to anti-kinks, which also bind the doped fermions at their respective centers. Out of this symmetry line, we show that quasi-spiral profiles appear with a characteristic wavevector set by the density k=2πρk = 2πρ, providing non-perturbative evidence for chiral spirals beyond the large-N limit. These results demonstrate that various exotic inhomogeneous phases can arise in lattice field theories, and motivate the use of quantum simulators to confirm such QCD-inspired phenomena in future experiments.

Rényi and Shannon mutual information in critical and decohered critical system

Authors: Yoshihito Kuno, Takahiro Orito, Ikuo Ichinose

arXiv ID: 2506.18475 | Date: 2025-06-23

Abstract: We investigate a critical many-body system by introducing a Rényi generalized mutual information, connecting between Rényi mutual information and Rényi Shannon mutual information. This Rényi generalized mutual information can offer more experimentally accessible alternative than the conventional entanglement entropy. As a critical many-body state, we focus on the critical transverse-field Ising model (TFIM) described by the Ising conformal field theory (CFT). We show that even if we modify the non-selective projective measurement assumed in Rényi Shannon mutual information by replacing the measurement into decoherence by environment, the Rényi generalized Shannon mutual information maintains the CFT properties such as subsystem CFT scaling law and its central charge observed through both the conventional Rényi Shannon mutual information and Rényi mutual information. Furthermore, we apply a local decoherence to the critical ground state of the TFIM and numerically observe the Rényi generalized mutual information by changing the parameter controlling environment effect (corresponding to the strength of measurement) in the Rényi generalized mutual information and the strength of the decoherence to which the entire system subjects. We find that Rényi-22 type central charge connected to the central charge is fairly robust, indicating the strong robustness of the Ising CFT properties against local decoherence by environment.

Accelerating Photonic Integrated Circuit Design: Traditional, ML and Quantum Methods

Authors: Alessandro Daniele Genuardi Oquendo, Ali Nadir, Tigers Jonuzi, Siddhartha Patra, Nilotpal Kanti Sinha, Román Orús, Sam Mugel

arXiv ID: 2506.18435 | Date: 2025-06-23

Abstract: Photonic Integrated Circuits (PICs) provide superior speed, bandwidth, and energy efficiency, making them ideal for communication, sensing, and quantum computing applications. Despite their potential, PIC design workflows and integration lag behind those in electronics, calling for groundbreaking advancements. This review outlines the state of PIC design, comparing traditional simulation methods with machine learning approaches that enhance scalability and efficiency. It also explores the promise of quantum algorithms and quantum-inspired methods to address design challenges.

Qumode Tensor Networks for False Vacuum Decay in Quantum Field Theory

Authors: Steven Abel, Michael Spannowsky, Simon Williams

arXiv ID: 2506.17388 | Date: 2025-06-20

Abstract: False vacuum decay in scalar quantum field theory (QFT) is a cornerstone of early Universe cosmology and high energy physics, yet its real-time dynamics is essentially inaccessible to classical computation due to its non-perturbative, highly entangled dynamics. We introduce a general Hamiltonian framework for simulating full interacting QFTs, using a spatial lattice of continuos-variable ``qumodes'' -- bosonic local oscillators whose high-dimensional local Hilbert space faithfully captures interacting field dynamics. This construction is rooted in continuous-variable quantum computing (CVQC), and provides a unified platform spanning efficient classical tensor-network methods and emerging photonic quantum hardware. The first key advance of this work is a robust and scaleable method for preparing the QFT in its correct initial vacuum state. We develop an imaginary-time preparation algorithm tailored to qumode lattices, that efficiently projects onto the vacuum even in strongly coupled regimes. This provides a controllable starting point for studying nonperturbative dynamics such as tunnelling and real-time decay. Building on this, we use a time-evolving block decimation algorithm to capture the real-time dynamics of the scalar field. Our second key advance is the identification and excitation of the negative fluctuation mode of the bounce configuration on the qumode lattice. A small displacement along this mode produces the expected tachyonic growth, driving fully coherent bubble nucleation without requiring classically supercritical seeds. This demonstrates that the qumode lattice captures non-perturbative quantum dynamics that lie beyond the classical treatments. Our results establish the qumode network as a scalable framework for non-equilibrium scalar QFT phenomena and pave the way for higher-dimensional studies and continuous-variable quantum computing implementations.

Tensor network calculation of boundary and corner magnetization

Authors: Roman Krcmar, Jozef Genzor, Andrej Gendiar, Tomotoshi Nishino

arXiv ID: 2506.17194 | Date: 2025-06-20

Abstract: The Corner Transfer Matrix Renormalization Group (CTMRG) algorithm is modified to measure the magnetization at the boundary of the system, including the corners of the square-shaped lattice. Using automatic differentiation, we calculate the magnetization's first derivative, allowing us to determine the boundary critical exponent ββ accurately.

Phase Transition of the Ising Model on a 3-Dimensional Fractal Lattice

Authors: Jozef Genzor, Roman Krčmár, Hiroshi Ueda, Denis Kochan, Andrej Gendiar, Tomotoshi Nishino

arXiv ID: 2506.17053 | Date: 2025-06-20

Abstract: The critical behavior of the classical Ising model on a three-dimensional fractal lattice with Hausdorff dimension dH=ln32/ln4=2.5d_H = \ln32 / \ln4 = 2.5 is investigated using the higher-order tensor renormalization group (HOTRG) method. We determine the critical temperature Tc2.65231T_c \approx 2.65231 and the critical exponents for magnetization β0.059β\approx 0.059 and field response δ35δ\approx 35. Unlike a previously studied 2D fractal with dH1.792d_H \approx 1.792, the specific heat for this 3D fractal exhibits a divergent singularity at TcT_c. The results are compared with those for regular lattices and other fractal structures to elucidate the role of dimensionality in critical phenomena.

Rigorous Maximum Likelihood Estimation for Quantum States

Authors: Kuchibhotla Aditi, Stephen Becker

arXiv ID: 2506.16646 | Date: 2025-06-19

Abstract: Existing quantum state tomography methods are limited in scalability due to their high computation and memory demands, making them impractical for recovery of large quantum states. In this work, we address these limitations by reformulating the maximum likelihood estimation (MLE) problem using the Burer-Monteiro factorization, resulting in a non-convex but low-rank parameterization of the density matrix. We derive a fully unconstrained formulation by analytically eliminating the trace-one and positive semidefinite constraints, thereby avoiding the need for projection steps during optimization. Furthermore, we determine the Lagrange multiplier associated with the unit-trace constraint a priori, reducing computational overhead. The resulting formulation is amenable to scalable first-order optimization, and we demonstrate its tractability using limited-memory BFGS (L-BFGS). Importantly, we also propose a low-memory version of the above algorithm to fully recover certain large quantum states with Pauli-based POVM measurements. Our low-memory algorithm avoids explicitly forming any density matrix, and does not require the density matrix to have a matrix product state (MPS) or other tensor structure. For a fixed number of measurements and fixed rank, our algorithm requires just O(dlogd)\mathcal{O}(d \log d) complexity per iteration to recover a d×dd \times d density matrix. Additionally, we derive a useful error bound that can be used to give a rigorous termination criterion. We numerically demonstrate that our method is competitive with state-of-the-art algorithms for moderately sized problems, and then demonstrate that our method can solve a 20-qubit problem on a laptop in under 5 hours.

Theory of multi-qubit superradiance in a waveguide in the presence of finite delay times

Authors: Sofia Arranz Regidor, Franco Nori, Stephen Hughes

arXiv ID: 2506.16605 | Date: 2025-06-19

Abstract: We study the quantum dynamics of multiple two-level atoms (qubits) in a waveguide quantum electrodynamics system, with a focus on modified superradiance effects between two or four atoms with finite delay times. Using a numerically exact matrix product approach, we explore both Markovian and non-Markovian regimes, and highlight the significant influence of time-delayed feedback effects and the clear breakdown of assuming instantaneous coupling dynamics. We first show a system composed of two spatially separated qubits, prepared in a doubly excited state (both fully excited), and provide a comprehensive study of how delayed feedback influences the collective system decay rates, as well as the quantum correlations between waveguide photons, atoms, and between atom and photons. The system is then extended to include two additional qubits located next to the initial ones (four qubits in total), and we demonstrate, by manipulating the initial excitations and the time-delay effects, how long-term quantum correlations and light-matter entangled states can be established.

QMetro++ -- Python optimization package for large scale quantum metrology with customized strategy structures

Authors: Piotr Dulian, Stanisław Kurdziałek, Rafał Demkowicz-Dobrzański

arXiv ID: 2506.16524 | Date: 2025-06-19

Abstract: QMetro++ is a Python package containing a set of tools dedicated to identifying optimal estimation protocols that maximize quantum Fisher information (QFI). Optimization can be performed for an arbitrary arrangement of input states, parameter encoding channels, noise correlations, control operations and measurements. The use of tensor networks and iterative see-saw algorithm allows for an efficient optimization even in the regime of large number of channel uses (N100N\approx100). Additionally, the package comes with an implementation of the recently developed methods for computing fundamental upper bounds on QFI, which serve as benchmarks of optimality of the outcomes of numerical optimization. All functionalities are wrapped up in a user-friendly interface which enables defining strategies at various levels of detail.

Joint Tensor-Train Parameterization for Efficient and Expressive Low-Rank Adaptation

Authors: Jun Qi, Chen-Yu Liu, Sabato Marco Siniscalchi, Chao-Han Huck Yang, Min-Hsiu Hsieh

arXiv ID: 2506.16456 | Date: 2025-06-19

Abstract: Low-Rank Adaptation (LoRA) is widely recognized for its parameter-efficient fine-tuning of large-scale neural models. However, standard LoRA independently optimizes low-rank matrices, which inherently limits its expressivity and generalization capabilities. While classical tensor-train (TT) decomposition can be separately employed on individual LoRA matrices, this work demonstrates that the classical TT-based approach neither significantly improves parameter efficiency nor achieves substantial performance gains. This paper proposes TensorGuide, a novel tensor-train-guided adaptation framework to overcome these limitations. TensorGuide generates two correlated low-rank LoRA matrices through a unified TT structure driven by controlled Gaussian noise. The resulting joint TT representation inherently provides structured, low-rank adaptations, significantly enhancing expressivity, generalization, and parameter efficiency without increasing the number of trainable parameters. Theoretically, we justify these improvements through neural tangent kernel analyses, demonstrating superior optimization dynamics and enhanced generalization. Extensive experiments on quantum dot classification and GPT-2 fine-tuning benchmarks demonstrate that TensorGuide-based LoRA consistently outperforms standard LoRA and TT-LoRA, achieving improved accuracy and scalability with fewer parameters.

Quantum disordered ground state and relative proximity to an exactly solvable model in the frustrated magnet CeMgAl11_{11}O19_{19}

Authors: G. Bastien, A. Eliáš, V. Anderle, A. Kancko, C. A. Corrêa, S. Kumar, P. Proschek, J. Prokleška, L. Nádherný, D. Sedmidubský, T. Treu, P. Gegenwart, M. Kratochvílová, M. Žonda, R. H. Colman

arXiv ID: 2506.16207 | Date: 2025-06-19

Abstract: The magnetic properties of the triangular magnet CeMgAl11_{11}O19_{19} were investigated by magnetization and specific heat measurements down to T=0.03T=0.03\,K on single crystals grown by the floating zone method. The formation of effective spins Seff=1/2S_\mathrm{eff}= 1/2 below T<10T < 10\,K was confirmed both by DFT calculations and specific heat measurements. No magnetic order was found down to T=0.03T=0.03\,K despite the formation of magnetic correlations observed in specific heat. The measured magnetization was compared with DMRG computation and their agreement supports the proposal of a strongly anisotropic magnetic interaction antiferromagnetically coupling the spin components in the abab plane and ferromagnetically coupling the spin component along the cc axis. However, our quantitative study of the magnetization indicates a weaker proximity to quantum criticality between ferromagnetism and antiferromagnetism than the previous inelastic neutron scattering study. Finally, we propose that the absence of magnetic order in CeMgAl11_{11}O19_{19} would most probably be related to the structural disorder revealed by single-crystal X-ray diffraction.

Superfluid dome in the spatially modulated two-dimensional XY model

Authors: Feng-Feng Song, Aditya Chugh, Hanggai Nuomin, Naoki Kawashima, Alexander Wietek

arXiv ID: 2506.16068 | Date: 2025-06-19

Abstract: In strongly correlated electron systems, superconductivity and charge density waves often coexist in close proximity, suggesting a deeper relationship between these competing phases. Recent research indicates that these orders can intertwine, with the superconducting order parameter coupling to modulations in the electronic density. To elucidate this interplay, we study a two-dimensional XY model with a periodic modulation of the coupling strength in one spatial direction. Using a combination of tensor network methods and Monte Carlo simulations, we reveal a non-monotonic, dome-like dependence of TcT_c on the modulation wavelength, with the peak TcT_c shifting to longer wavelengths as the modulation strength grows. The origin of this phenomenon is traced back to an effective pinning of vortices in the valleys of the modulation, confirmed by a comparison to modulated qq-state clock models. These findings shed new light on the phase behavior of intertwined superconducting and charge-ordered states, offering a deeper understanding of their complex interactions.

A Scalable Factorization Approach for High-Order Structured Tensor Recovery

Authors: Zhen Qin, Michael B. Wakin, Zhihui Zhu

arXiv ID: 2506.16032 | Date: 2025-06-19

Abstract: Tensor decompositions, which represent an NN-order tensor using approximately NN factors of much smaller dimensions, can significantly reduce the number of parameters. This is particularly beneficial for high-order tensors, as the number of entries in a tensor grows exponentially with the order. Consequently, they are widely used in signal recovery and data analysis across domains such as signal processing, machine learning, and quantum physics. A computationally and memory-efficient approach to these problems is to optimize directly over the factors using local search algorithms such as gradient descent, a strategy known as the factorization approach in matrix and tensor optimization. However, the resulting optimization problems are highly nonconvex due to the multiplicative interactions between factors, posing significant challenges for convergence analysis and recovery guarantees. In this paper, we present a unified framework for the factorization approach to solving various tensor decomposition problems. Specifically, by leveraging the canonical form of tensor decompositions--where most factors are constrained to be orthonormal to mitigate scaling ambiguity--we apply Riemannian gradient descent (RGD) to optimize these orthonormal factors on the Stiefel manifold. Under a mild condition on the loss function, we establish a Riemannian regularity condition for the factorized objective and prove that RGD converges to the ground-truth tensor at a linear rate when properly initialized. Notably, both the initialization requirement and the convergence rate scale polynomially rather than exponentially with NN, improving upon existing results for Tucker and tensor-train format tensors.

Clifford augmented density matrix renormalization group for \textit{ab initio} quantum chemistry

Authors: Lizhong Fu, Honghui Shang, Jinlong Yang, Chu Guo

arXiv ID: 2506.16026 | Date: 2025-06-19

Abstract: The recently proposed Clifford augmented density matrix renormalization group (CA-DMRG) method seamlessly integrates Clifford circuits with matrix product states, and takes advantage of the expression power from both. CA-DMRG has been shown to be able to achieve higher accuracy than standard DMRG on commonly used lattice models, with only moderate computational overhead compared to the latter. In this work, we propose an efficient scheme in CA-DMRG to deal with \textit{ab initio} quantum chemistry Hamiltonians, and apply it to study several molecular systems. Our numerical results show that CA-DMRG can reach higher accuracy than DMRG using the same bond dimension, pointing out a promising route to push the boundary of solving \textit{ab initio} quantum chemistry with strong static correlations.

Unconventional Spin Dynamics and Supersolid Excitations in the Triangular-Lattice XXZ Model

Authors: Rafael Flores-Calderón, Roderich Moessner, Frank Pollmann

arXiv ID: 2506.15516 | Date: 2025-06-18

Abstract: Motivated by recent experiments, we investigate the spin-1/2 XXZ model on the triangular lattice with strong Ising anisotropy, combining large-scale numerical simulations and analytical methods to uncover unconventional spin dynamics. First, we compute the dynamical spin structure factor using density matrix renormalization group (DMRG) simulations and find excellent agreement with inelastic neutron scattering data on the layered compound K2Co(SeO3)2\text{K}_2\text{Co}(\text{SeO}_3)_2. The low-energy spectrum reveals a roton-like minimum at the MM point, absent in linear spin-wave theory, accompanied by peak intensity and a broad continuum above it. Near the ΓΓ point, we observe an approximately linear dispersion with vanishing spectral weight. Second, we compare two analytical frameworks that reproduce the observed features. The first is a hard-core boson approach, which includes: (i) an effective staggered boson model (ESBM) at zero magnetic field, (ii) perturbation theory applied to the one-third magnetization plateau, and (iii) a self-consistent mean-field Schwinger boson theory (SBT). The second framework is based on a variational supersolid quantum dimer model (QDM) ansatz, combined with a single-mode approximation. The SBT captures the broad continuum, the MM-point minimum, and linear dispersion at ΓΓ, whereas the QDM reproduces the roton minimum and linear dispersion at finite momentum near ΓΓ. Remarkably, both the QDM wavefunction and the DMRG ground state exhibit nearly identical structure factors with pronounced transverse photon-like excitations. Together, our comprehensive theoretical and numerical analysis elucidates the microscopic origin of supersolid excitations in the XXZ triangular lattice model and their proximity to a spin liquid phase observed experimentally.

Thermalization from quantum entanglement: jet simulations in the massive Schwinger model

Authors: Adrien Florio, David Frenklakh, Sebastian Grieninger, Dmitri E. Kharzeev, Andrea Palermo, Shuzhe Shi

arXiv ID: 2506.14983 | Date: 2025-06-17

Abstract: We investigate the emergence of thermalization in a quantum field-theoretic model mimicking the production of jets in QCD -- the massive Schwinger model coupled to external sources. Specifically, we compute the expectation values of local operators as functions of time and compare them to their thermal counterparts, quantify the overlap between the evolving density matrix and the thermal one, and compare the dynamics of the energy-momentum tensor to predictions from relativistic hydrodynamics. Through these studies, we find that the system approaches thermalization at late times and elucidate the mechanisms by which quantum entanglement drives thermalization in closed field-theoretic systems. Our results show how thermodynamic behavior emerges in real time from unitary quantum dynamics.

Path Integral Monte Carlo in the Angular Momentum Basis for a Chain of Planar Rotors

Authors: Estêvão de Oliveira, Muhammad Shaeer Moeed, Pierre-Nicholas Roy

arXiv ID: 2506.14977 | Date: 2025-06-17

Abstract: We introduce a Path Integral Monte Carlo (PIMC) approach that uses the angular momentum representation for the description of interacting rotor systems. Such a choice of representation allows the calculation of momentum properties without having to break the paths. The discrete nature of the momentum basis also allows the use of rejection-free Gibbs sampling techniques. To illustrate the method, we study the collective behavior of NN confined planar rotors with dipole-dipole interactions, a system known to exhibit a quantum phase transition from a disordered to an ordered state at zero temperature. Ground state properties are obtained using the Path Integral Ground State (PIGS) method. We propose a Bond-Hamiltonian decomposition for the high temperature density matrix factorization of the imaginary time propagator. We show that \textit{cluster-loop} type moves are necessary to overcome ergodicity issues and to achieve efficient Markov Chain updates. Ground state energies and angular momentum properties are computed and compared with Density Matrix Renormalization Group (DMRG) benchmark results. In particular, the derivative of the kinetic energy with respect to the interaction strength estimator is presented as a successful order parameter for the detection of the quantum phase transition.

Zigzag antiferromagnets in the SU(3) Hubbard model on the square lattice

Authors: Stijn V. Kleijweg, Philippe Corboz

arXiv ID: 2506.14703 | Date: 2025-06-17

Abstract: SU(N) Hubbard models exhibit a rich variety of phases, which may be realized through quantum simulation with ultracold atomic gases in optical lattices. In this work we study the Mott insulating phases of the SU(3) Hubbard model at 1/3-filling using infinite projected entangled-pair states, optimized with both imaginary time evolution and variational optimization. In the limit of strong interactions we reproduce the antiferromagnetic 3-sublattice ordered state previously identified in the SU(3) Heisenberg model. At intermediate interaction strength we find antiferromagnetic states exhibiting zigzag patterns of different lengths, in agreement with previous Hartree-Fock and constrained-path auxiliary-field quantum Monte Carlo calculations. We study the color order parameter and energy anisotropy, which are discontinuous across the phase transitions. Finally, we analyze the different energy contributions in two competing phases, identifying low-energy bonds at the corners of the zigzag that help stabilize the zigzag states.

Enhancing Symbolic Machine Learning by Subsymbolic Representations

Authors: Stephen Roth, Lennart Baur, Derian Boer, Stefan Kramer

arXiv ID: 2506.14569 | Date: 2025-06-17

Abstract: The goal of neuro-symbolic AI is to integrate symbolic and subsymbolic AI approaches, to overcome the limitations of either. Prominent systems include Logic Tensor Networks (LTN) or DeepProbLog, which offer neural predicates and end-to-end learning. The versatility of systems like LTNs and DeepProbLog, however, makes them less efficient in simpler settings, for instance, for discriminative machine learning, in particular in domains with many constants. Therefore, we follow a different approach: We propose to enhance symbolic machine learning schemes by giving them access to neural embeddings. In the present paper, we show this for TILDE and embeddings of constants used by TILDE in similarity predicates. The approach can be fine-tuned by further refining the embeddings depending on the symbolic theory. In experiments in three real-world domain, we show that this simple, yet effective, approach outperforms all other baseline methods in terms of the F1 score. The approach could be useful beyond this setting: Enhancing symbolic learners in this way could be extended to similarities between instances (effectively working like kernels within a logical language), for analogical reasoning, or for propositionalization.

High-expressibility Quantum Neural Networks using only classical resources

Authors: Marco Maronese, Francesco Ferrari, Matteo Vandelli, Daniele Dragoni

arXiv ID: 2506.13605 | Date: 2025-06-16

Abstract: Quantum neural networks (QNNs), as currently formulated, are near-term quantum machine learning architectures that leverage parameterized quantum circuits with the aim of improving upon the performance of their classical counterparts. In this work, we show that some desired properties attributed to these models can be efficiently reproduced without necessarily resorting to quantum hardware. We indeed study the expressibility of parametrized quantum circuit commonly used in QNN applications and contrast it to those of two classes of states that can be efficiently simulated classically: matrix-product states (MPS), and Clifford-enhanced MPS (CMPS), obtained by applying a set of Clifford gates to MPS. In addition to expressibility, we assess the level of primary quantum resources, entanglement and non-stabilizerness (a.k.a. "magic"), in random ensembles of such quantum states, tracking their convergence to the Haar distribution. While MPS require a large number of parameters to reproduce an arbitrary quantum state, we find that CMPS approach the Haar distribution more rapidly, in terms of both entanglement and magic. Our results indicate that high expressibility in QNNs is attainable with purely classical resources.

TensorSLM: Energy-efficient Embedding Compression of Sub-billion Parameter Language Models on Low-end Devices

Authors: Mingxue Xu, Yao Lei Xu, Danilo P. Mandic

arXiv ID: 2506.13514 | Date: 2025-06-16

Abstract: Small Language Models (SLMs, or on-device LMs) have significantly fewer parameters than Large Language Models (LLMs). They are typically deployed on low-end devices, like mobile phones and single-board computers. Unlike LLMs, which rely on increasing model size for better generalisation, SLMs designed for edge applications are expected to have adaptivity to the deployment environments and energy efficiency given the device battery life constraints, which are not addressed in datacenter-deployed LLMs. This paper addresses these two requirements by proposing a training-free token embedding compression approach using Tensor-Train Decomposition (TTD). Each pre-trained token embedding vector is converted into a lower-dimensional Matrix Product State (MPS). We comprehensively evaluate the extracted low-rank structures across compression ratio, language task performance, latency, and energy consumption on a typical low-end device, i.e. Raspberry Pi. Taking the sub-billion parameter versions of GPT-2/Cerebres-GPT and OPT models as examples, our approach achieves a comparable language task performance to the original model with around 2.0×2.0\times embedding layer compression, while the energy consumption of a single query drops by half.

Excitations and dynamical structure factor of J1J2J_1-J_2 spin-3/23/2 and spin-5/25/2 Heisenberg spin chains

Authors: Aman Sharma, Mithilesh Nayak, Natalia Chepiga, Frédéric Mila

arXiv ID: 2506.13431 | Date: 2025-06-16

Abstract: We study the dynamical structure factor of the frustrated spin-3/23/2 J1J_1-J2J_2 Heisenberg chains, with particular focus on the partially dimerized phase that emerges between two Kosterlitz-Thouless transitions. Using a valence bond solid ansatz corroborated by density matrix renormalization group simulations, we investigate the nature of magnon and spinon excitations through the single-mode approximation. We show that the magnon develops an incommensurate dispersion at J20.32J1J_2 \approx 0.32J_1, while the spinons, viewed as domain walls between degenerate valence bond solid states, become incommensurate at J20.4J1J_2 \approx 0.4J_1 beyond the Lifshitz point (J20.388J1J_2 \approx 0.388J_1). The dynamical structure factor exhibits rich spectral features shaped by the interplay between these excitations, with magnons appearing as resonances embedded in the spinon continuum. The spinon gap shows a nonmonotonic behavior, reaching a peak near the center of the partially dimerized phase and closing at the boundaries, suggesting the appearance of a floating phase as a result of the condensation of incommensurate spinons. Comparative analysis with the spin-5/25/2 case confirms the universality of these phenomena across half-integer higher-spin systems. Our results provide detailed insight into how fractionalization and incommensurate condensation govern the spectral properties of frustrated spin chains, offering a unified picture across different spin magnitudes.

Entanglement-minimized orbitals enable faster quantum simulation of molecules

Authors: Zhendong Li

arXiv ID: 2506.13386 | Date: 2025-06-16

Abstract: Quantum computation offers significant potential for accelerating the simulation of molecules and materials through algorithms such as quantum phase estimation (QPE). However, the expected speedup in ground-state energy estimation depends critically on the ability to efficiently prepare an initial state with high overlap with the true ground state. For strongly correlated molecules such as iron-sulfur clusters, this overlap is demonstrated to decay exponentially with system size. To alleviate this problem, we introduce an efficient classical algorithm to find entanglement-minimized orbitals (EMOs) using spin-adapted matrix product states (MPS) with small bond dimensions. The EMO basis yields a more compact ground-state representation, significantly easing initial state preparation for challenging systems. Our algorithm improves initial state overlap by nearly an order of magnitude over prior orbital optimization approaches for an iron-sulfur cluster with four irons, and is scalable to larger systems with many unpaired electrons, including the P-cluster and FeMo-cofactor in nitrogenase with eight transition metal centers. For these systems, we achieve substantial enhancements on initial state overlap by factors of O(102)O(10^2) and O(105)O(10^5), respectively, compared to results obtained using localized orbitals. Our results show that initial state preparation for these challenging systems requires far fewer resources than prior estimates suggested.

Compressing local vertex functions from the multipoint numerical renormalization group using quantics tensor cross interpolation

Authors: Markus Frankenbach, Marc Ritter, Mathias Pelz, Nepomuk Ritz, Jan von Delft, Anxiang Ge

arXiv ID: 2506.13359 | Date: 2025-06-16

Abstract: The multipoint numerical renormalization group (mpNRG) is a powerful impurity solver that provides accurate spectral data useful for computing local, dynamic correlation functions in imaginary or real frequencies non-perturbatively across a wide range of interactions and temperatures. It gives access to a local, non-perturbative four-point vertex in imaginary and real frequencies, which can be used as input for subsequent computations such as diagrammatic extensions of dynamical mean--field theory. However, computing and manipulating the real-frequency four-point vertex on large, dense grids quickly becomes numerically challenging when the density and/or the extent of the frequency grid is increased. In this paper, we compute four-point vertices in a strongly compressed quantics tensor train format using quantics tensor cross interpolation, starting from discrete partial spectral functions obtained from mpNRG. This enables evaluations of the vertex on frequency grids with resolutions far beyond the reach of previous implementations. We benchmark this approach on the four-point vertex of the single-impurity Anderson model across a wide range of physical parameters, both in its full form and its asymptotic decomposition. For imaginary frequencies, the full vertex can be represented to an accuracy on the order of 21032\cdot 10^{-3} with maximum bond dimensions not exceeding 120. The more complex full real-frequency vertex requires maximum bond dimensions not exceeding 170 for an accuracy of 2%\lesssim 2\%. Our work marks another step toward tensor-train-based diagrammatic calculations for correlated electronic lattice models starting from a local, non-perturbative mpNRG vertex.

Scalable Simulation of Quantum Many-Body Dynamics with Or-Represented Quantum Algebra

Authors: Lukas Broers, Rong-Yang Sun, Seiji Yunoki

arXiv ID: 2506.13241 | Date: 2025-06-16

Abstract: High-performance numerical methods are essential not only for advancing quantum many-body physics but also for enabling integration with emerging quantum computing platforms. We present a scalable and general-purpose parallel algorithm for quantum simulations based on or-represented quantum algebra (ORQA). This framework applies to arbitrary spin systems and naturally integrates with quantum circuit simulation in the Heisenberg picture, particularly relevant to recent large-scale experiments on superconducting qubit processors [Kim et al., Nature 618, 500 (2023)]. As a benchmark, we simulate the kicked Ising model on a 127-qubit heavy-hexagon lattice, tracking the time evolution of local magnetization using up to one trillion Pauli strings. Executed on the supercomputer Fugaku, our simulations exhibit strong scaling up to 2172^{17} parallel processes with near-linear communication overhead. These results establish ORQA as a practical and high-performance tool for quantum many-body dynamics, and highlight its potential for integration into hybrid quantum-classical computational frameworks, complementing recent advances in tensor-network and surrogate simulation techniques.

Diagnosing 2D symmetry protected topological states via mixed state anomaly

Authors: Chao Xu, Yunlong Zang, Yixin Ma, Yingfei Gu, Shenghan Jiang

arXiv ID: 2506.13096 | Date: 2025-06-16

Abstract: Symmetry-protected topological (SPT) phases are short-range entangled quantum states characterized by anomalous edge behavior, a manifestation of the bulk-boundary correspondence for topological phases. Moreover, the Li-Haldane conjecture posits that the entanglement spectrum exhibits the same anomaly as the physical edge spectrum, thereby serving as an entanglement-based fingerprint for identifying topological phases. In this work, we extend the entanglement-based diagnostic tools by demonstrating that the edge anomaly is manifested not only in the entanglement spectrum but also in the reduced density matrix itself, a phenomenon we refer to as the mixed state anomaly. Focusing on the two-dimensional Z2\mathbb{Z}_2 SPT phase, we show that this anomaly is subtly encoded in symmetry-twisted mixed states, leading to a topological contribution to the disorder parameter beyond the area law, as well as a spontaneous-symmetry-breaking type long-range order when time reversal symmetry is present.

The Software Landscape for the Density Matrix Renormalization Group

Authors: Per Sehlstedt, Jan Brandejs, Paolo Bientinesi, Lars Karlsson

arXiv ID: 2506.12629 | Date: 2025-06-14

Abstract: The density matrix renormalization group (DMRG) algorithm is a cornerstone computational method for studying quantum many-body systems, renowned for its accuracy and adaptability. Despite DMRG's broad applicability across fields such as materials science, quantum chemistry, and quantum computing, numerous independent implementations have been developed. This survey maps the rapidly expanding DMRG software landscape, providing a comprehensive comparison of features among 35 existing packages. We found significant overlap in features among the packages when comparing key aspects, such as parallelism strategies for high-performance computing and symmetry-adapted formulations that enhance efficiency. This overlap suggests opportunities for modularization of common operations, including tensor operations, symmetry representations, and eigensolvers, as the packages are mostly independent and share few third-party library dependencies where functionality is factored out. More widespread modularization and standardization would result in reduced duplication of efforts and improved interoperability. We believe that the proliferation of packages and the current lack of standard interfaces and modularity are more social than technical. We aim to raise awareness of existing packages, guide researchers in finding a suitable package for their needs, and help developers identify opportunities for collaboration, modularity standardization, and optimization. Ultimately, this work emphasizes the value of greater cohesion and modularity, which would benefit DMRG software, allowing these powerful algorithms to tackle more complex and ambitious problems.

Accelerated Inchworm Method with Tensor-Train Bath Influence Functional

Authors: Geshuo Wang, Yixiao Sun, Siyao Yang, Zhenning Cai

arXiv ID: 2506.12410 | Date: 2025-06-14

Abstract: We propose an efficient tensor-train-based algorithm for simulating open quantum systems with the inchworm method, where the reduced dynamics of the open quantum system is expressed as a perturbative series of high-dimensional integrals. Instead of evaluating the integrals with Monte Carlo methods, we approximate the costly bath influence functional (BIF) in the integrand as a tensor train, allowing accurate deterministic numerical quadrature schemes implemented in an iterative manner. Thanks to the low-rank structure of the tensor train, our proposed method has a complexity that scales linearly with the number of dimensions. Our method couples seamlessly with the tensor transfer method, allowing long-time simulations of the dynamics.

Simulating the Antiferromagnetic Heisenberg Model on a Spin-Frustrated Kagome Lattice with the Contextual Subspace Variational Quantum Eigensolver

Authors: Tim Weaving, Alexis Ralli, Vinul Wimalaweera, Peter J. Love, Peter V. Coveney

arXiv ID: 2506.12391 | Date: 2025-06-14

Abstract: In this work we investigate the ground state properties of a candidate quantum spin liquid using a superconducting Noisy Intermediate-Scale Quantum (NISQ) device. Specifically, we study the antiferromagnetic Heisenberg model on a Kagome lattice, a geometrically frustrated structure that gives rise to a highly degenerate energy spectrum. To successfully simulate this system, we employ a qubit reduction strategy leveraging the Contextual Subspace methodology, significantly reducing the problem size prior to execution on the quantum device. We improve the quality of these subspaces by using the wavefunctions obtained from low bond dimension Density Matrix Renormalization Group (DMRG) calculations to bias the subspace stabilizers through a symplectic approximate symmetry generator extraction algorithm. Reducing the Hamiltonian size allows us to implement tiled circuit ensembles and deploy the Variational Quantum Eigensolver (VQE) to estimate the ground state energy. We adopt a hybrid quantum error mitigation strategy combining Readout Error Mitigation (REM), Symmetry Verification (SV) and Zero Noise Extrapolation (ZNE). This approach yields high-accuracy energy estimates, achieving error rates on the order of 0.01% and thus demonstrating the potential of near-term quantum devices for probing frustrated quantum materials.

Universal Spreading of Nonstabilizerness and Quantum Transport

Authors: Emanuele Tirrito, Poetri Sonya Tarabunga, Devendra Singh Bhakuni, Marcello Dalmonte, Piotr Sierant, Xhek Turkeshi

arXiv ID: 2506.12133 | Date: 2025-06-13

Abstract: We investigate how transport properties of U(1)U(1)-conserving dynamics impact the growth of quantum resources characterizing the complexity of many-body states. We quantify wave-function delocalization using participation entropy (PE), a measure rooted in the coherence theory of pure states, and assess nonstabilizerness through stabilizer Rényi entropy (SRE). Focusing on the XXZ spin chain initialized in domain-wall state, we demonstrate universal power-law growth of both PE and SRE, with scaling exponents explicitly reflecting the underlying transport regimes, ballistic, diffusive, or KPZ-type superdiffusive. Our results establish a solid connection between quantum resources and transport, providing insights into the dynamics of complexity within symmetry-constrained quantum systems.

Improved Ground State Estimation in Quantum Field Theories via Normalising Flow-Assisted Neural Quantum States

Authors: Vishal S. Ngairangbam, Michael Spannowsky, Timur Sypchenko

arXiv ID: 2506.12128 | Date: 2025-06-13

Abstract: We propose a hybrid variational framework that enhances Neural Quantum States (NQS) with a Normalising Flow-based sampler to improve the expressivity and trainability of quantum many-body wavefunctions. Our approach decouples the sampling task from the variational ansatz by learning a continuous flow model that targets a discretised, amplitude-supported subspace of the Hilbert space. This overcomes limitations of Markov Chain Monte Carlo (MCMC) and autoregressive methods, especially in regimes with long-range correlations and volume-law entanglement. Applied to the transverse-field Ising model with both short- and long-range interactions, our method achieves comparable ground state energy errors with state-of-the-art matrix product states and lower energies than autoregressive NQS. For systems up to 50 spins, we demonstrate high accuracy and robust convergence across a wide range of coupling strengths, including regimes where competing methods fail. Our results showcase the utility of flow-assisted sampling as a scalable tool for quantum simulation and offer a new approach toward learning expressive quantum states in high-dimensional Hilbert spaces.

Knapsack and Shortest Path Problems Generalizations From A Quantum-Inspired Tensor Network Perspective

Authors: Sergio Muñiz Subiñas, Jorge Martínez Martín, Alejandro Mata Ali, Javier Sedano, Ángel Miguel García-Vico

arXiv ID: 2506.11711 | Date: 2025-06-13

Abstract: In this paper, we present two tensor network quantum-inspired algorithms to solve the knapsack and the shortest path problems, and enables to solve some of its variations. These methods provide an exact equation which returns the optimal solution of the problems. As in other tensor network algorithms for combinatorial optimization problems, the method is based on imaginary time evolution and the implementation of restrictions in the tensor network. In addition, we introduce the use of symmetries and the reutilization of intermediate calculations, reducing the computational complexity for both problems. To show the efficiency of our implementations, we carry out some performance experiments and compare the results with those obtained by other classical algorithms.

The Integral Decimation Method for Quantum Dynamics and Statistical Mechanics

Authors: Ryan T. Grimm, Alexander J. Staat, Joel D. Eaves

arXiv ID: 2506.11341 | Date: 2025-06-12

Abstract: The solutions to many problems in the mathematical, computational, and physical sciences often involve multidimensional integrals. A direct numerical evaluation of the integral incurs a computational cost that is exponential in the number of dimensions, a phenomenon called the curse of dimensionality. The problem is so substantial that one usually employs sampling methods, like Monte Carlo, to avoid integration altogether. Here, we derive and implement a quantum algorithm to compress a multidimensional integrand into a product of matrix-valued functions - a spectral tensor train - changing the computational complexity of integration from exponential to polynomial. The algorithm compresses the integrand by applying a sequence of quantum gates to an unentangled quantum state, where each term corresponds to a body-ordered term in the potential. Because it allows for the systematic elimination of small contributions to the integral through decimation, we call the method integral decimation. The functions in the spectral basis are analytically differentiable and integrable, and in applications to the partition function, integral decimation numerically factorizes an interacting system into a product of noninteracting ones. We illustrate integral decimation by evaluating the absolute free energy and entropy of a chiral XY model as a continuous function of temperature. We also compute the nonequilibrium time-dependent reduced density matrix of a quantum chain with between two and forty levels, each coupled to colored noise. When other methods provide numerical solutions to these models, they quantitatively agree with integral decimation. When conventional methods become intractable, integral decimation can be a powerful alternative.

Quantum Fisher information from tensor network integration of Lyapunov equation

Authors: Gabriela Wójtowicz, Susana F. Huelga, Marek M. Rams, Martin B. Plenio

arXiv ID: 2506.11330 | Date: 2025-06-12

Abstract: The Quantum Fisher Information (QFI) is a geometric measure of state deformation calculated along the trajectory parameterizing an ensemble of quantum states. It serves as a key concept in quantum metrology, where it is linked to the fundamental limit on the precision of the parameter that we estimate. However, the QFI is notoriously difficult to calculate due to its non-linear mathematical form. For mixed states, standard numerical procedures based on eigendecomposition quickly become impractical with increasing system size. To overcome this limitation, we introduce a novel numerical approach based on Lyapunov integrals that combines the concept of symmetric logarithmic derivative and tensor networks. Importantly, this approach requires only the elementary matrix product states algorithm for time-evolution, opening a perspective for broad usage and application to many-body systems. We discuss the advantages and limitations of our methodology through an illustrative example in quantum metrology, where the thermal state of the transverse-field Ising model is used to measure magnetic field amplitude.

Free Probability in a Minimal Quantum Circuit Model

Authors: Felix Fritzsch, Pieter W. Claeys

arXiv ID: 2506.11197 | Date: 2025-06-12

Abstract: Recent experimental and theoretical developments in many-body quantum systems motivate the study of their out-of-equilibrium properties through multi-time correlation functions. We consider the dynamics of higher-order out-of-time-order correlators (OTOCs) in a minimal circuit model for quantum dynamics. This model mimics the dynamics of a structured subsystem locally coupled to a maximally random environment. We prove the exponential decay of all higher-order OTOCs and fully characterize the relevant time scales, showing how local operators approach free independence at late times. We show that the effects of the environment on the local subsystem can be captured in a higher-order influence matrix, which allows for a Markovian description of the dynamics provided an auxiliary degree of freedom is introduced. This degree of freedom directly yields a dynamical picture for the OTOCs in terms of free cumulants from free probability, consistent with recent predictions from the full eigenstate thermalization hypothesis (ETH). This approach and the relevant influence matrix are expected to be applicable in more general settings and present a first step to characterizing quantum memory in higher-order OTOCs.

Kibble-Zurek dynamical scaling hypothesis in the Google analog-digital quantum simulator of the XXXX model

Authors: Yintai Zhang, Francis A. Bayocboc, Jacek Dziarmaga

arXiv ID: 2506.10771 | Date: 2025-06-12

Abstract: State-of-the-art tensor networks are employed to simulate the Hamiltonian ramp in the analog-digital quantum simulation of the quantum phase transition to the quasi-long-range ordered phase of the two-dimensional square-lattice XXXX model [T.I. Andersen \textit{et al.}, Nature (London) \textbf{638}, 79 (2025)]. We focus on the quantum Kibble-Zurek (KZ) mechanism near the quantum critical point. Using the infinite projected entangled pair state, we simulate an infinite lattice and demonstrate the KZ scaling hypothesis for the XXXX correlations across a wide range of ramp times. We use the time-dependent variational principle algorithm to simulate a finite 8×88\times 8 lattice, similar to the one in the quantum simulation, and find that adiabatic finite-size effects dominate for longer ramp times, where the correlation length's growth with increasing ramp time saturates and the excitation energy's dependence on the ramp time crosses over to a power-law decay characteristic of adiabatic transitions. This finding contradicts the quantum simulation data where the correlation length seems to obey KZ-like power laws, although with modified exponents.

Multi-entropy and the Dihedral Measures at Quantum Critical Points

Authors: Jonathan Harper, Ali Mollabashi, Tadashi Takayanagi, Kenya Tasuki

arXiv ID: 2506.10396 | Date: 2025-06-12

Abstract: The multi-entropy and dihedral measures are a class of tractable measures for multi-partite entanglement, which are labeled by the Rényi index (or replica number) nn as in the Rényi entanglement entropy. The purpose of this article is to demonstrate that these quantities are new useful probes of quantum critical points by examining concrete examples. In particular, we compute the multi-entropy and dihedral measures in the 1+11+1 dimensional massless free scalar field theory on a lattice and in the transverse-field Ising model. For n=2n=2, we find that the numerical results in both lattice theories quantitatively agree with those from conformal field theoretic calculations. For n=3n=3 and n=4n=4, we provide new predictions of these measures for the massless scalar field theory.

Coupled Lindblad pseudomode theory for simulating open quantum systems

Authors: Zhen Huang, Gunhee Park, Garnet Kin-Lic Chan, Lin Lin

arXiv ID: 2506.10308 | Date: 2025-06-12

Abstract: Coupled Lindblad pseudomode theory is a promising approach for simulating non-Markovian quantum dynamics on both classical and quantum platforms, with dynamics that can be realized as a quantum channel. We provide theoretical evidence that the number of coupled pseudomodes only needs to scale as polylog(T/ε)\mathrm{polylog}(T/\varepsilon) in the simulation time TT and precision ε\varepsilon. Inspired by the realization problem in control theory, we also develop a robust numerical algorithm for constructing the coupled modes that avoids the non-convex optimization required by existing approaches. We demonstrate the effectiveness of our method by computing population dynamics and absorption spectra for the spin-boson model. This work provides a significant theoretical and computational improvement to the coupled Lindblad framework, which impacts a broad range of applications from classical simulations of quantum impurity problems to quantum simulations on near-term quantum platforms.

Worldline deconfinement and emergent long-range interaction in entanglement Hamiltonian and entanglement spectrum

Authors: Zenan Liu, Zhe Wang, Dao-Xin Yao, Zheng Yan

arXiv ID: 2506.10078 | Date: 2025-06-11

Abstract: When a system exhibits a bulk gap but gapless edge states (e.g., a symmetry-protected topological phase), the entanglement spectrum (ES) resembles the energy spectrum on virtual edge, that is the Li-Haldane conjecture. In this way, the ES plays an important probe to detect the topological phases according to this bulk-edge correspondence. When a system is fully gapped, both in bulk and edge, the ES still remains similar to the virtual edge spectrum which can be explained by the recently proposed wormhole effect in the path integral of reduced density matrix. However, what will happen in the ES when the system is fully gapless? We find that though the ES roughly seems like an edge energy spectrum, and it actually contains relevant long-range interaction which modifies the intrinsic physics of entanglement Hamiltonian (EH). Moreover, the mechanism of short-/long-range interaction in EH can be understood as the confinement/deconfinement of worldlines in a path integral of reduced density matrix. Our work demonstrates that the gapless mode can induce a long-range interaction in EH.

Entanglement Holography in Quantum Phases via Twisted Rényi-N Correlators

Authors: Pablo Sala, Frank Pollmann, Masaki Oshikawa, Yizhi You

arXiv ID: 2506.10076 | Date: 2025-06-11

Abstract: We introduce a holographic framework for the entanglement Hamiltonian in symmetry-protected topological (SPT) phases with area-law entanglement, whose reduced density matrix ρeHeρ\propto e^{-H_e} can be treated as a lower-dimensional mixed state. By replicating ρρ, we reconstruct the fixed-point SPT wavefunction, establishing an exact correspondence between the bulk strange correlator of the (d+1)-dimensional SPT state and the twisted Rényi-N operator of the d-dimensional reduced density matrix. Notably, the reduced density matrix exhibits long-range or quasi-long-range order along the replica direction, revealing a universal entanglement feature in SPT phases. As a colloary, we generalized the framework of twisted Rényi-N correlator to thermal states and open quantum systems, providing an alternative formulation of the Lieb-Schultz-Mattis theorem, applicable to both closed and open systems. Finally, we extend our protocol to mixed-state SPT phases and introduce new quantum information metrics -- twisted Rényi-N correlators of the surgery operator -- to characterize the topology of mixed states.

Hollow-grams: Generalized Entanglement Wedges from the Gravitational Path Integral

Authors: Sami Kaya, Pratik Rath, Kyle Ritchie

arXiv ID: 2506.10064 | Date: 2025-06-11

Abstract: Recently, Bousso and Penington (BP) made a proposal for the entanglement wedge associated to a gravitating bulk region. In this paper, we derive this proposal in time-reflection symmetric settings using the gravitational path integral. To do this, we exploit the connection between random tensor networks (RTNs) and fixed-geometry states in gravity. We define the entropy of a bulk region in an RTN by removing tensors in that region and computing the entropy of the open legs thus generated in the "hollowed" RTN. We thus derive the BP proposal for RTNs and hence, also for fixed-geometry states in gravity. By then expressing a general holographic state as a superposition over fixed-geometry states and using a diagonal approximation, we provide a general gravitational path integral derivation of the BP proposal. We demonstrate that the saddles computing the Rényi entropy SnS_n depend on how the bulk region is gauge-invariantly specified. Nevertheless, we show that the BP proposal is universally reproduced in the n1n\to1 limit.

Entanglement structure for finite system under dual-unitary dynamics

Authors: Gaurav Rudra Malik, Rohit Kumar Shukla, Sudhanva Joshi, S. Aravinda, Sunil Kumar Mishra

arXiv ID: 2506.09904 | Date: 2025-06-11

Abstract: The dynamics of quantum many-body systems in the chaotic regime are of particular interest due to the associated phenomena of information scrambling and entanglement generation within the system. While these systems are typically intractable using traditional numerical methods, an effective framework can be implemented based on dual-unitary circuits which have emerged as a minimal model for maximally chaotic dynamics. In this work, we investigate how individual two-body operators influence the global dynamics of circuits composed of dual-unitaries. We study their effect on entanglement generation while examining it from both bipartite and multipartite perspectives. Here we also highlight the significant role of local unitaries in the dynamics when paired with operators from the dual-unitary class, showing that systems with identical entangling power can exhibit a range of differing entanglement growth rates. Furthermore, we present calculations establishing time-step-dependent lower bounds, which depend on both the initial state and the entangling power of the constituent operators. Finally, we find that time-evolving an initial state composed of pair products generates a state with nearly maximal multipartite entanglement content, approaching the bounds established by Absolutely Maximally Entangled (AME) states.

Quantum Algorithm Software for Condensed Matter Physics

Authors: T. Farajollahpour

arXiv ID: 2506.09308 | Date: 2025-06-11

Abstract: This report offers a comprehensive analysis of the evolving landscape of quantum algorithm software specifically tailored for condensed matter physics. It examines fundamental quantum algorithms such as Variational Quantum Eigensolver (VQE), Quantum Phase Estimation (QPE), Quantum Annealing (QA), Quantum Approximate Optimization Algorithm (QAOA), and Quantum Machine Learning (QML) as applied to key condensed matter problems including strongly correlated systems, topological phases, and quantum magnetism. This review details leading software development kits (SDKs) like Qiskit, Cirq, PennyLane, and Q\#, and profiles key academic, commercial, and governmental initiatives driving innovation in this domain. Furthermore, it assesses current challenges, including hardware limitations, algorithmic scalability, and error mitigation, and explores future trajectories, anticipating new algorithmic breakthroughs, software enhancements, and the impact of next-generation quantum hardware. The central theme emphasizes the critical role of a co-design approach, where algorithms, software, and hardware evolve in tandem, and highlights the necessity of standardized benchmarks to accelerate progress towards leveraging quantum computation for transformative discoveries in condensed matter physics.

(2+1)d Lattice Models and Tensor Networks for Gapped Phases with Categorical Symmetry

Authors: Kansei Inamura, Sheng-Jie Huang, Apoorv Tiwari, Sakura Schafer-Nameki

arXiv ID: 2506.09177 | Date: 2025-06-10

Abstract: Gapped phases in 2+1 dimensional quantum field theories with fusion 2-categorical symmetries were recently classified and characterized using the Symmetry Topological Field Theory (SymTFT) approach arXiv:2408.05266, arXiv:2502.20440. In this paper, we provide a systematic lattice model construction for all such gapped phases. Specifically, we consider "all-boson type" fusion 2-category symmetries, all of which are obtainable from 0-form symmetry groups GG (possibly with an 't Hooft anomaly) via generalized gauging--that is, by stacking with an HH-symmetric TFT and gauging a subgroup HH. The continuum classification directly informs the lattice data, such as the generalized gauging that determines the symmetry category, and the data that specifies the gapped phase. We construct commuting projector Hamiltonians and ground states applicable to any non-chiral gapped phase with such symmetries. We also describe the ground states in terms of tensor networks. In light of the length of the paper, we include a self-contained summary section presenting the main results and examples.

Digital Quantum Simulation of the Kitaev Quantum Spin Liquid

Authors: Seongjun Park, Eun-Gook Moon

arXiv ID: 2506.09156 | Date: 2025-06-10

Abstract: The ground state of the Kitaev quantum spin liquid on a honeycomb lattice is an intriguing many-body state characterized by its topological order and massive entanglement. One of the significant issues is to prepare and manipulate the ground state as well as excited states in a quantum simulator. Here, we provide a protocol to manipulate the Kitaev quantum spin liquid via digital quantum simulation. A series of unitary gates for the protocol is explicitly constructed, showing its circuit depth is an order of O(N) with the number of qubits, N. We demonstrate the efficiency of our protocol on the IBM Heron r2 processor for N = 8 and 12. We further validate our theoretical framework through numerical simulations, confirming high-fidelity quantum state control for system sizes up to N = 450, and discuss the possible implications of these results.

MetaTT: A Global Tensor-Train Adapter for Parameter-Efficient Fine-Tuning

Authors: Javier Lopez-Piqueres, Pranav Deshpande, Archan Ray, Mattia J. Villani, Marco Pistoia, Niraj Kumar

arXiv ID: 2506.09105 | Date: 2025-06-10

Abstract: We present MetaTT, a Tensor Train (TT) adapter framework for fine-tuning of pre-trained transformers. MetaTT enables flexible and parameter-efficient model adaptation by using a single shared TT to factorize transformer sub-modules. This factorization indexes key structural dimensions, including layer and matrix type, and can optionally incorporate heads and tasks. This design allows MetaTT's parameter count to scale with the sum, rather than the product, of the modes, resulting in a substantially more compact adapter. Our benchmarks compare MetaTT with LoRA along with recent state-of-the-art matrix and tensor decomposition based fine-tuning methods. We observe that when tested on single-task standard language modeling benchmarks, MetaTT achieves competitive parameter efficiency to accuracy tradeoff. We further demonstrate that MetaTT performs competitively when compared to state-of-the-art methods on multi-task learning. Finally, we leverage the TT-ansatz to design a rank adaptive optimizer inspired by the DMRG method from many-body physics. Our results demonstrate that integrating this approach with AdamW enhances optimization performance for a specified target rank.

Matrix Product State on a Quantum Computer

Authors: Yong Liu, Guangyao Huang, Yizhi Wang, Junjie Wu

arXiv ID: 2506.08395 | Date: 2025-06-10

Abstract: Solving quantum many-body systems is one of the most significant regimes where quantum computing applies. Currently, as a hardware-friendly computational paradigms, variational algorithms are often used for finding the ground energy of quantum many-body systems. However, running large-scale variational algorithms is challenging, because of the noise as well as the obstacle of barren plateaus. In this work, we propose the quantum version of matrix product state (qMPS), and develop variational quantum algorithms to prepare it in canonical forms, allowing to run the variational MPS method, which is equivalent to the Density Matrix Renormalization Group method, on near term quantum devices. Compared with widely used methods such as variational quantum eigensolver, this method can greatly reduce the number of qubits used in local optimization, and thus mitigate the effects of barren plateaus while obtaining better accuracy. Our method holds promise for distributed quantum computing, offering possibilities for fusion of different computing systems.

Neuralized Fermionic Tensor Networks for Quantum Many-Body Systems

Authors: Si-Jing Du, Ao Chen, Garnet Kin-Lic Chan

arXiv ID: 2506.08329 | Date: 2025-06-10

Abstract: We describe a class of neuralized fermionic tensor network states (NN-fTNS) that introduce non-linearity into fermionic tensor networks through configuration-dependent neural network transformations of the local tensors. The construction uses the fTNS algebra to implement a natural fermionic sign structure and is compatible with standard tensor network algorithms, but gains enhanced expressivity through the neural network parametrization. Using the 1D and 2D Fermi-Hubbard models as benchmarks, we demonstrate that NN-fTNS achieve order of magnitude improvements in the ground-state energy compared to pure fTNS with the same bond dimension, and can be systematically improved through both the tensor network bond dimension and the neural network parametrization. Compared to existing fermionic neural quantum states (NQS) based on Slater determinants and Pfaffians, NN-fTNS offer a physically motivated alternative fermionic structure. Furthermore, compared to such states, NN-fTNS naturally exhibit improved computational scaling and we demonstrate a construction that achieves linear scaling with the lattice size.

Microscopic Mechanism of Anyon Superconductivity Emerging from Fractional Chern Insulators

Authors: Fabian Pichler, Clemens Kuhlenkamp, Michael Knap, Ashvin Vishwanath

arXiv ID: 2506.08000 | Date: 2025-06-09

Abstract: Fractional quantum Hall (FQH) states and superconductors typically require contrasting conditions, yet recent experiments have observed them in the same device. A natural explanation is that mobile anyons give rise to superconductivity; however, this mechanism requires binding of minimally charged anyons to establish an unusual energy hierarchy. This scenario has mostly been studied with effective theories, leaving open the question of how anyon superconductivity can arise from repulsive interactions. Here, we show that such an energy hierarchy of anyons arises naturally in fractional Chern insulators (FCIs) at fillings ν=2/(4p1)ν= 2/(4p \mp 1) when they are driven toward a quantum phase transition into a ``semion crystal'' -- an exotic charge-density-wave (CDW) insulator with semion topological order. Near the transition, Cooper-pair correlations are enhanced, so that a conventional charge-2e superconductor appears with doping. Guided by these insights, we analyze a microscopic realization in a repulsive Hubbard-Hofstadter model. Tensor network simulations at ν=2/3ν= 2/3 reveal a robust FCI that, with increasing interactions, transitions into the semion crystal. Finding a stable semion crystal in such a minimal model highlights it as a viable state competing with conventional CDW and FQH states. In the vicinity of this transition, we find markedly enhanced Cooper pairing, consistent with our theory that the 2e/3 anyon is cheaper than a pair of isolated e/3 anyons. Doping near the transition should in general lead to doping Cooper pairs and charge-2e superconductivity, with chiral edge modes of alternating central charge c=±2c = \pm2, which can coexist with translation symmetry breaking. Our framework unifies recent approaches to anyon superconductivity, reconciles it with strong repulsion and provides guidance for flat band moiré materials such as recent experiments in twisted MoTe2_2.

Microscopic Mechanism of Anyon Superconductivity Emerging from Fractional Chern Insulators

Authors: Fabian Pichler, Clemens Kuhlenkamp, Michael Knap, Ashvin Vishwanath

arXiv ID: 2506.08000 | Date: 2025-06-09

Abstract: Fractional quantum Hall (FQH) states and superconductors typically require contrasting conditions, yet recent experiments have observed them in the same device. A natural explanation is that mobile anyons give rise to superconductivity; however, this mechanism requires binding of minimally charged anyons to establish an unusual energy hierarchy. This scenario has mostly been studied with effective theories, leaving open the question of how anyon superconductivity can arise from repulsive interactions. Here, we show that such an energy hierarchy of anyons arises naturally in fractional Chern insulators (FCIs) at fillings ν=2/(4p1)ν= 2/(4p \mp 1) when they are driven toward a quantum phase transition into a ``semion crystal'' -- an exotic charge-density-wave (CDW) insulator with semion topological order. Near the transition, Cooper-pair correlations are enhanced, so that a conventional charge-2e superconductor appears with doping. Guided by these insights, we analyze a microscopic realization in a repulsive Hubbard-Hofstadter model. Tensor network simulations at ν=2/3ν= 2/3 reveal a robust FCI that, with increasing interactions, transitions into the semion crystal. Finding a stable semion crystal in such a minimal model highlights it as a viable state competing with conventional CDW and FQH states. In the vicinity of this transition, we find markedly enhanced Cooper pairing, consistent with our theory that the 2e/3 anyon is cheaper than a pair of isolated e/3 anyons. Doping near the transition should in general lead to doping Cooper pairs and charge-2e superconductivity, with chiral edge modes of alternating central charge c=±2c = \pm2, which can coexist with translation symmetry breaking. Our framework unifies recent approaches to anyon superconductivity, reconciles it with strong repulsion and provides guidance for flat band moiré materials such as recent experiments in twisted MoTe2_2.

Scaling up the transcorrelated density matrix renormalization group

Authors: Benjamin Corbett, Akimasa Miyake

arXiv ID: 2506.07441 | Date: 2025-06-09

Abstract: Explicitly correlated methods, such as the transcorrelated method which shifts a Jastrow or Gutzwiller correlator from the wave function to the Hamiltonian, are designed for high-accuracy calculations of electronic structures, but their application to larger systems has been hampered by the computational cost. We develop improved techniques for the transcorrelated density matrix renormalization group (DMRG), in which the ground state of the transcorrelated Hamiltonian is represented as a matrix product state (MPS), and demonstrate large-scale calculations of the ground-state energy of the two-dimensional Fermi-Hubbard model. Our developments stem from three technical inventions: (i) constructing matrix product operators (MPO) of transcorrelated Hamiltonians with low bond dimension and high sparsity, (ii) exploiting the entanglement structure of the ground states to increase the accuracy of the MPS representation, and (iii) optimizing the non-linear parameter of the Gutzwiller correlator to mitigate the non-variational nature of the transcorrelated method. We examine systems of size up to 12×1212 \times 12 lattice sites, four times larger than previous transcorrelated DMRG studies, and demonstrate that transcorrelated DMRG yields significant improvements over standard non-transcorrelated DMRG for equivalent computational effort. Transcorrelated DMRG reduces the error of the ground state energy by 3×3\times-17×17 \times, with the smallest improvement seen for a small system at half-filling and the largest improvement in a dilute closed-shell system.

One-Shot Simulation of Static Disorder in Quantum Dynamics with Equilibrium Initial State via Matrix Product State Sampling

Authors: Zhao Zhang, Jiajun Ren, Wei-Hai Fang

arXiv ID: 2506.07120 | Date: 2025-06-08

Abstract: Static disorder plays a crucial role in the electronic dynamics and spectroscopy of complex molecular systems. Traditionally, obtaining observables averaged over static disorder requires thousands of realizations via direct sampling of the disorder distribution, leading to high computational costs. In this work, we extend the auxiliary degree-of-freedom based matrix product state (MPS) method to handle system-bath correlated thermal equilibrium initial states. We validate the effectiveness of the extended method by computing the dipole-dipole time correlation function of the Holstein model relevant to the emission spectrum of molecular aggregates. Our results show that the method accurately captures static disorder effects using a one-shot quantum dynamical simulation, with only a moderate increase in MPS bond dimension, thereby significantly reducing computational cost. Moreover, it enables the generation of a much larger number of samples than the conventional direct sampling method at negligible additional cost, thus reducing statistical errors. This method provides a broadly useful tool for calculating equilibrium time correlation functions in system-bath coupled models with static disorder.

Disorder and the Robustness of Superconductivity on the Flat Band

Authors: Si Min Chan, Benoît Grémaud, G. George Batrouni

arXiv ID: 2506.07095 | Date: 2025-06-08

Abstract: We study the interplay between on-site disorder and fermion pairing on the quasi one-dimensional flat band Creutz lattice. Both disorder and flat bands localize particles, but an attractive interaction results in pair formation and delocalization giving rise to superconductivity. In this work, we examine the attractive Hubbard model on the Creutz lattice to study the competition between these two effects and elucidate the properties of the superconducting phase and the localization quantum phase transition as the disorder strength is increased. Our main result is that flat band superconductivity is robust against disorder: The critical disorder strength, WcW_c, required to localize the fermion pairs and destroy superconductivity, is finite at any interaction strength, UU, and is proportional to the superconducting weight, DsD_s, of the clean system. Using large scale density matrix renormalization group computations, we show that this transition is of the BKT form. In addition, even at very small interaction strength, the localization is not due to single fermion localization but to pair localization. For completeness, we briefly study this disorder-induced localization with mean field theory and show that WcW_c can be accurately determined by using an appropriate scaling function.

Emergent Holographic Spacetime from Quantum Information

Authors: Tadashi Takayanagi

arXiv ID: 2506.06595 | Date: 2025-06-07

Abstract: Holographic duality describes gravitational theories in terms of quantum many-body systems. In holography, quantum information theory provides a crucial tool that directly connects microscopic structures of these systems to the geometries of gravitational spacetimes. One manifestation is that the entanglement entropy in quantum many-body systems can be calculated from the area of an extremal surface in the corresponding gravitational spacetime. This implies that a gravitational spacetime can emerge from an enormous number of entangled qubits. In this Essay, I will discuss open problems in this area of research, considering recent developments and outlining future prospects towards a complete understanding of quantum gravity. The first step in this direction is to understand what kind of quantum circuits each holographic spacetime corresponds to, drawing on recent developments in quantum complexity theories and studying concrete examples of holography in string theory. Next, we should extend the concept of holography to general spacetimes, e.g., those spacetimes which appear in realistic cosmologies, by utilizing the connections between quantum information and holography. To address the fundamental question of how time emerges, I will propose the concepts of pseudo-entropy and time-like entanglement as a useful tool in our exploration.

Angular kk-uniformity and the Hyperinvariance of Holographic Codes

Authors: Wanli Cheng

arXiv ID: 2506.06577 | Date: 2025-06-06

Abstract: Holographic quantum error-correcting codes, often realized through tensor network architectures, have emerged as compelling toy models for exploring bulk-boundary duality in AdS-CFT. By encoding bulk information into highly entangled boundary degrees of freedom, they capture key features of holography such as subregion duality, operator reconstruction, and complementary recovery. Among them, hyperinvariant tensor networks-characterized by the inclusion of edge tensors and the enforcement of multi-tensor isometries-offer a promising platform for realizing features such as state dependence and nontrivial boundary correlations. However, existing constructions are largely confined to two-dimensional regular tilings, and the structural principles underlying hyperinvariance remain poorly understood, especially in higher dimensions. To address this, we introduce a geometric criterion called angular k-uniformity, which refines standard k-uniformity and its planar variants by requiring isometric behavior within angular sectors of a tensor's rotationally symmetric layout. This condition enables the systematic identification and construction of hyperinvariant holographic codes on regular hyperbolic honeycombs in arbitrary dimension, and extends naturally to heterogeneous networks and qLEGO architectures beyond regular tilings. Altogether, angular k-uniformity provides a versatile, geometry-aware framework for analyzing and designing holographic tensor networks and codes with hyperinvariant features such as nontrivial boundary correlations and state-dependent complementary recovery.

Real-time Estimators for Scattering Observables: A full account of finite volume errors for quantum simulation

Authors: Ivan M. Burbano, Marco A. Carrillo, Rana Urek, Anthony N. Ciavarella, Raúl A. Briceño

arXiv ID: 2506.06511 | Date: 2025-06-06

Abstract: The real-time correlators of quantum field theories can be directly probed through new approaches to simulation, such as quantum computing and tensor networks. This provides a new framework for computing scattering observables in lattice formulations of strongly interacting theories, such as lattice quantum chromodynamics. In this paper, we prove that the proposal of real-time estimators of scattering observables is universally applicable to all scattering observables of gapped quantum field theories. All finite-volume errors are exponentially suppressed, and the rate of this suppression is controlled by the regulator considered, namely, a displacement of the spectrum of the theory into the complex plane. A partial restoration of Lorentz symmetry by averaging over different boosts gives an additional suppression of finite volume errors. Our results also apply to the simulation of wavepacket scattering, where a similar averaging is performed to construct the wavepackets that regulate the finite volume effects. We also comment on potential applications of our results to traditional computational schemes.

Compression, simulation, and synthesis of turbulent flows with tensor trains

Authors: Stefano Pisoni, Raghavendra Dheeraj Peddinti, Egor Tiunov, Siddhartha E. Guzman, Leandro Aolita

arXiv ID: 2506.05477 | Date: 2025-06-05

Abstract: Numerical simulations of turbulent fluids are paramount to real-life applications, from predicting and modeling flows to diagnostic purposes in engineering. However, they are also computationally challenging due to their intrinsically non-linear dynamics, which requires a very high spatial resolution to accurately describe them. A promising idea is to represent flows on a discrete mesh using tensor trains (TTs), featuring a convenient scaling of the number of parameters with the mesh size. However, it is yet not clear how the compression power of TTs is affected by the complexity of the flows, measured by the Reynolds number. In fact, no TT fluid solver has been extensively validated in a fully developed turbulent regime yet. We fill this gap. We conduct a comprehensive analysis of TTs as an Ansatz to compress, simulate, and synthetically generate fiducial turbulent snapshots in 3D. Specifically, first, we exhaustively investigate the effect of TT compression of given snapshots on key turbulence signatures, including the energy spectrum and different accuracy metrics. Second, we present a TT solver to simulate time evolution of 3D fluid fields according to the incompressible Navier-Stokes equations entirely within the compressed representation. Third, we develop a TT algorithm to generate artificial snapshots displaying all the signatures of turbulence. In all three cases, a number of parameters scaling polylogarithmically with the mesh size is enough for accurate descriptions. Our findings confirm that fluids in truly turbulent regimes admit an efficient TT description and offer a powerful, quantum-inspired toolkit for their computational treatment.

A 2D-CFT Factory: Critical Lattice Models from Competing Anyon Condensation Processes in SymTO/SymTFT

Authors: Ling-Yan Hung, Kaixin Ji, Ce Shen, Yidun Wan, Yu Zhao

arXiv ID: 2506.05324 | Date: 2025-06-05

Abstract: In this paper, we introduce a ``CFT factory'' : a novel algorithm of methodically generating 2D lattice models that would flow to 2D conformal fixed points in the infrared. These 2D models are realised by giving critical boundary conditions to 3D topological orders (symTOs/symTFTs) described by string-net models, often called the strange correlators. We engineer these critical boundary conditions by introducing a commensurate amount of non-commuting anyon condensates. The non-invertible symmetries preserved at the critical point can be controlled by studying a novel ``refined condensation tree''. Our structured method generates an infinite family of critical lattice models, including the A-series minimal models, and uncovers previously unknown critical points. Notably, we find at least three novel critical points (c1.3\approx 1.3, 1.81.8, and 2.52.5 respectively) preserving the Haagerup symmetries, in addition to recovering previously reported ones. The condensation tree, together with a generalised Kramers-Wannier duality, predicts precisely large swathes of phase boundaries, fixes almost completely the global phase diagram, and sieves out second order phase transitions. This is not only illustrated in well-known examples (such as the 8-vertex model related to the A5A_5 category) but also further verified with precision numerics, using our improved (non-invertible) symmetry-preserving tensor-network RG, in novel examples involving the Haagerup symmetries. We show that critical couplings can be precisely encoded in the categorical data (Frobenius algebras and quantum dimensions in unitary fusion categories), thus establishing a powerful, systematic route to discovering and potentially classifying new conformal field theories.

Tensor network method for real-space topology in quasicrystal Chern mosaics

Authors: Tiago V. C. Antão, Yitao Sun, Adolfo O. Fumega, Jose L. Lado

arXiv ID: 2506.05230 | Date: 2025-06-05

Abstract: Computing topological invariants in two-dimensional quasicrystals and super-moire matter is a remarkable open challenge, due to the absence of translational symmetry and the colossal number of sites inherent to these systems. Here, we establish a method to compute local topological invariants of exceptionally large systems using tensor networks, enabling the computation of invariants for Hamiltonians with hundreds of millions of sites, several orders of magnitude above the capabilities of conventional methodologies. Our approach leverages a tensor-network representation of the density matrix using a Chebyshev tensor network algorithm, enabling large-scale calculations of topological markers in quasicrystalline and moire systems. We demonstrate our methodology with two-dimensional quasicrystals featuring C8C_8 and C10C_{10} rotational symmetries and mosaics of Chern phases. Our work establishes a powerful method to compute topological phases in exceptionally large-scale topological systems, providing the required tool to rationalize generic supe-moire and quasicrystalline topological matter.

Discrete quantum systems from topological field theory

Authors: Daniel S. Freed, Michael J. Hopkins, Constantin Teleman

arXiv ID: 2506.05131 | Date: 2025-06-05

Abstract: We introduce a technique to construct gapped lattice models using defects in topological field theory. We illustrate with 2+1 dimensional models, for example Chern-Simons theories. These models are local, though the state space is not necessarily a tensor product of vector spaces over the complex numbers. The Hamiltonian is a sum of commuting projections. We also give a topological field theory construction of Levin-Wen models.

Hybrid between biologically inspired and quantum inspired many-body states

Authors: Miha Srdinšek, Xavier Waintal

arXiv ID: 2506.05050 | Date: 2025-06-05

Abstract: Deep neural networks can represent very different sorts of functions, including complex quantum many-body states. Tensor networks can also represent these states, have more structure and are easier to optimize. However, they can be prohibitively costly computationally in two or higher dimensions. Here, we propose a generalization of the perceptron - the perceptrain - which borrows features from the two different formalisms. We construct variational many-body ansatz from a simple network of perceptrains. The network can be thought of as a neural network with a few distinct features inherited from tensor networks. These include efficient local optimization akin to the density matrix renormalization algorithm, instead of optimizing of all the parameters at once; the possibility to dynamically increase the number of parameters during the optimization; the possibility to compress the state to avoid overfitting; and a structure that remains quantum-inspired. We showcase the ansatz using a combination of Variational Monte-Carlo (VMC) and Green Function Monte-Carlo (GFMC) on a 10×1010\times 10 transverse field quantum Ising model with a long range 1/r61/r^6 antiferromagnetic interaction. The model corresponds to the Rydberg (cold) atoms platform proposed for quantum annealing. We consistently find a very high relative accuracy for the ground state energy, around 10510^{-5} for VMC and 10610^{-6} for GFMC in all regimes of parameters, including in the vicinity of the quantum phase transition. We used very small ranks (25\sim 2-5) of perceptrains, as opposed to multiples of thousand used in matrix product states. The optimization of the energy was robust with respect to the choice of initial conditions and hyper-parameters, in contrast to a common experience when using neural network wave functions.

A Fast, Accurate and Oscillation-free Spectral Collocation Solver for High-dimensional Transport Problems

Authors: Nicola Cavallini, Gianmarco Manzini, Daniele Funaro, Andrea Favalli

arXiv ID: 2506.04732 | Date: 2025-06-05

Abstract: Transport phenomena-describing the movement of particles, energy, or other physical quantities-are fundamental in various scientific disciplines, including nuclear physics, plasma physics, astrophysics, engineering, and the natural sciences. However, solving the associated seven-dimensional transport equations poses a significant computational challenge due to the curse of dimensionality. We introduce the Tensor Train Superconsistent Spectral (T2{^2}S2{^2}) solver to address this challenge, integrating Spectral Collocation for exponential convergence, Superconsistency for stabilization in transport-dominated regimes, and Tensor Train format for substantial data compression. T2{^2}S2{^2} enforces a dimension-wise superconsistent condition compatible with tensor structures, achieving extremely low compression ratios, in the order of (1012)(10^{-12}), while preserving spectral accuracy. Numerical experiments on linear problems demonstrate that T2{^2}S2{^2} can solve high-dimensional transport problems in minutes on standard hardware, making previously intractable problems computationally feasible. This advancement opens new avenues for efficiently and accurately modeling complex transport phenomena.

Exponential distillation of dominant eigenproperties

Authors: Bence Bakó, Tenzan Araki, Bálint Koczor

arXiv ID: 2506.04380 | Date: 2025-06-04

Abstract: Estimating observable expectation values in eigenstates of quantum systems has a broad range of applications and is an area where early fault-tolerant quantum computers may provide practical quantum advantage. We develop a hybrid quantum-classical algorithm that enables the estimation of an arbitrary observable expectation value in an eigenstate, given an initial state is supplied that has dominant overlap with the targeted eigenstate -- but may overlap with any other eigenstates. Our approach builds on, and is conceptually similar to purification-based error mitigation techniques; however, it achieves exponential suppression of algorithmic errors using only a single copy of the quantum state. The key innovation is that random time evolution is applied in the quantum computer to create an average mixed quantum state, which is then virtually purified with exponential efficacy. We prove rigorous performance guarantees and conclude that the complexity of our approach depends directly on the energy gap in the problem Hamiltonian and remarkably, can be compared to phase estimation combined with amplitude estimation in terms of its scaling with respect to a target precision. We demonstrate in a broad range of numerical simulations the applicability of our framework in near-term and early fault-tolerant settings. Furthermore, we demonstrate in a 100-qubit example that direct classical simulation of our approach enables the prediction of ground and excited state properties of quantum systems using tensor network techniques, which we recognize as a quantum-inspired classical approach.

Entanglement renormalization circuits for 2d2d Gaussian Fermion States

Authors: Sing Lam Wong, Andrew C. Potter

arXiv ID: 2506.04200 | Date: 2025-06-04

Abstract: The simulation of entangled ground-states of quantum materials remains challenging for classical computational methods in more than one spatial dimension, and is a prime target for quantum computational advantage. To this end, an important goal is to identify efficient quantum state preparation protocols that minimize the physical qubit number and circuit depth resources required to capture higher-dimensional quantum correlations. This work introduces a quantum circuit compression algorithm for Gaussian fermion states based on the multi-scale entanglement renormalization ansatz (MERA), which provides an exponential reduction in the circuit depth required to approximate highly-entangled ground-states relevant for quantum materials simulations. The algorithm, termed two-dimensional Gaussian MERA (2d2d GMERA), extends MERA techniques to compress higher-dimensional Gaussian states. Through numerical simulations of the Haldane model on a honeycomb lattice, the method is shown to accurately capture area-law entangled states including topologically trivial insulators, Chern insulators, and critical Dirac semimetals. While Gaussian states alone are classically simulable, this approach establishes empirical upper bounds on quantum resources needed to prepare free fermion states that are adiabatically connected to correlated ground states, providing guidance for implementing these protocols on near-term quantum devices and offering a foundation for simulating more complex quantum materials. Finally, we develop a novel fermion-to-qubit encoding scheme, based on an expanding 2d2d topological order, that enables implementing fermionic rotations via qubit Pauli rotations with constant Pauli weight independent of system size.

Violation of Luttinger's theorem in one-dimensional interacting fermions

Authors: Meng Gao, Yin Zhong

arXiv ID: 2506.04064 | Date: 2025-06-04

Abstract: Using the density matrix renormalization group method, we systematically investigate the evolution of the Luttinger integral in the one-dimensional generalized tt-VV model as a function of filling and interaction strength, and identify three representative phases. In the weak-coupling regime, the zero-frequency Green's function exhibits a branch-cut structure at the Fermi momentum, and the Luttinger integral accurately reflects the particle density, indicating that the Luttinger theorem holds. As the interaction increases, the spectral weight near the Fermi momentum is gradually suppressed. Interestingly, in the strong coupling regime near half-filling, this singularity is progressively destroyed, accompanied by the emergence of momentum-space zeros in the real part of the Green's function, leading to a novel non-Fermi liquid metallic phase beyond the classic Luttinger liquid paradigm, where the Luttinger surface is no longer defined by a single singularity. While finite spectral weight remains at the original Fermi momentum, the singularity gradually diminishes. Meanwhile, zeros with negligible spectral weight appear away from this momentum, significantly affecting the integral. At exact half-filling, a single-particle gap opens, and the Green's function becomes nearly vanishing across the entire momentum space, indicating the complete suppression of low-energy electronic states consistent with the nature of an insulating charge-density-wave phase. These results suggest that the breakdown of the Luttinger theorem is not triggered by a single mechanism, but rather results from the interplay between interaction-driven evolution of excitation modes and the breaking of particle-hole symmetry, ultimately leading to a continuous reconstruction of the generalized Fermi surface from topologically protected to correlation-driven.

Technical report on a quantum-inspired solver for simulating compressible flows

Authors: Raghavendra Dheeraj Peddinti, Stefano Pisoni, Egor Tiunov, Alessandro Marini, Leandro Aolita

arXiv ID: 2506.03833 | Date: 2025-06-04

Abstract: This document presents a quantum-inspired solver for 2D Euler equations, accepted at the final phase of the Airbus-BWM Group Quantum Computing Challenge (ABQCC) 2024. We tackle the case study of Quantum Solvers for Predictive Aeroacoustic and Aerodynamic modeling tasks. We propose a tensor network based solver that scales polylogarithmically with the mesh size, in both runtime and memory. This provides a promising avenue for tackling the curse of dimensionality that plagues the direct numerical simulations in the field of computational fluid dynamics.

Computational Complexity of Non-Hermitian Quantum Systems

Authors: Brian Barch, Daniel Lidar

arXiv ID: 2506.03435 | Date: 2025-06-03

Abstract: We analyze the computational power of non-Hermitian quantum dynamics, i.e., conditional time evolutions that arise when a quantum system is monitored and one postselects on a particular measurement record. We establish an approximate equivalence between post-selection and arbitrary non-Hermitian Hamiltonians. Namely, first we establish hardness in the following sense: Let U=eiHtU=e^{-iHt} be an NH gate on nn qubits whose smallest and largest singular values differ by at least 2poly(n)2^{-\text{poly}(n)}. Together with any universal set of unitary gates, the ability to apply such a gate lets one efficiently emulate postselection. The resulting model decides every language in PostBQP; hence, under standard complexity conjectures, fully scalable NH quantum computers are unlikely to be engineered. Second, we establish upper bounds which show that conversely, any non-Hermitian evolution can be written as a unitary on a system-meter pair followed by postselecting the meter. This ``purification'' is compact -- it introduces only O(δ2)O(δ^{2}) Trotter error per time step δδ -- so any NH model whose purification lies in a strongly simulable unitary family (e.g., Clifford, matchgate, or low-bond-dimension tensor-network circuits) remains efficiently simulable. Thus, non-Hermitian physics neither guarantees a quantum advantage nor precludes efficient classical simulation: its complexity is controlled by the singular-value radius of the evolution operator and by the structure of its unitary purification.

Theory of Angle Resolved Photoemission Spectroscopy of Altermagnetic Mott Insulators

Authors: Lorenzo Lanzini, Purnendu Das, Michael Knap

arXiv ID: 2506.03263 | Date: 2025-06-03

Abstract: Altermagnetism has emerged as an unconventional form of collinear magnetism with spatial rotational symmetries, that give rise to strongly spin-split bands despite of an underlying fully-compensated antiferromagnetic order. Here, we develop a theory for the Angle Resolved Photoemission Spectroscopy (ARPES) response of altermagnetic Mott insulators. Crucially, the spectrum does not simply reflect the non-interacting band structure, but instead a magnetic polaron is formed at low energies, that can be interpreted as a spinon-holon bound state. We develop a spinon-holon parton theory and predict a renormalized bandwidth that we confirm by tensor network simulations. We analyze the characteristic spin-split spectrum and identify a spin-dependent spectral weight of the magnetic polaron, resulting from the altermagnetic symmetry. Our work paves the way for a systematic study of doping effects and correlation phenomena in altermagnetic Mott insulators.

Tensor Renormalization Group Meets Computer Assistance

Authors: Nikolay Ebel, Tom Kennedy, Slava Rychkov

arXiv ID: 2506.03247 | Date: 2025-06-03

Abstract: Tensor renormalization group, originally devised as a numerical technique, is emerging as a rigorous analytical framework for studying lattice models in statistical physics. Here we introduce a new renormalization map - the 2x1 map - which coarse-grains the lattice anisotropically by a factor of two in one direction followed by a 90-degree rotation. We develop a novel graphical language that translates the action of the 2x1 map into a system of inequalities on tensor components, with rigorous estimates in the Hilbert-Schmidt norm. We define a finite-dimensional "bounding box" called the hat-tensor, and a master function governing its RG flow. Iterating this function numerically, we establish convergence to the high-temperature fixed point for tensors lying within a quantifiable neighborhood. Our main theorem shows that tensors with deviations bounded by 0.02 in 63 orthogonal sectors flow to the fixed point. We also apply the method to specific models - the 2D Ising and XY models - obtaining explicit bounds on their high-temperature phase. This work brings the Tensor RG program closer towards a rigorous, computer-assisted construction of critical fixed points.

Spin-chain multichannel Kondo model via image impurity boundary condition

Authors: Jordan Gaines, Guangjie Li, Jukka Väyrynen

arXiv ID: 2506.02399 | Date: 2025-06-03

Abstract: One of the signature observables for the electronic multichannel Kondo model is the impurity entropy, which was claimed to be found in J1J_1-J2J_2 Heisenberg chain with open boundary condition (OBC) and periodic boundary condition (PBC), respectively for the one-channel and two-channel case. However, it is not clear how to generalize OBC and PBC in Heisenberg chains to find the multichannel Kondo impurity entropy with more than two channels. In this paper, we demonstrate that the correct boundary condition for realizing multichannel Kondo physics in Heisenberg chains is the image impurity boundary condition (IIBC), which yields the expected impurity entropy, ln[(5+1)/2]\ln[(\sqrt{5}+1)/2] for the three-channel case and ln3\ln\sqrt{3} for the four-channel case. Moreover, the IIBC reduces to OBC for the one-channel case and to PBC for the two-channel case. With IIBC, the finite-size scaling of the impurity entropy and the total spin both match the finite-temperature correction in the electronic multichannel Kondo model. Additionally, we show that the XXZ anisotropy reduces the impurity entropy through a power law of the effective Luttinger liquid parameter.

Quantum Complexity and Chaos in Many-Qudit Doped Clifford Circuits

Authors: Beatrice Magni, Xhek Turkeshi

arXiv ID: 2506.02127 | Date: 2025-06-02

Abstract: We investigate the emergence of quantum complexity and chaos in doped Clifford circuits acting on qudits of odd prime dimension dd. Using doped Clifford Weingarten calculus and a replica tensor network formalism, we derive exact results and perform large-scale simulations in regimes challenging for tensor network and Pauli-based methods. We begin by analyzing generalized stabilizer entropies, computable magic monotones in many-qudit systems, and identify a dynamical phase transition in the doping rate, marking the breakdown of classical simulability and the onset of Haar-random behavior. The critical behavior is governed by the qudit dimension and the magic content of the non-Clifford gate. Using the qudit TT-gate as a benchmark, we show that higher-dimensional qudits converge faster to Haar-typical stabilizer entropies. For qutrits (d=3d=3), analytical predictions match numerics on brickwork circuits, showing that locality plays a limited role in magic spreading. We also examine anticoncentration and entanglement growth, showing that O(logN)O(\log N) non-Clifford gates suffice for approximating Haar expectation values to precision ε\varepsilon, and relate antiflatness measures to stabilizer entropies in qutrit systems. Finally, we analyze out-of-time-order correlators and show that a finite density of non-Clifford gates is needed to induce chaos, with a sharp transition fixed by the local dimension, twice that of the magic transition. Altogether, these results establish a unified framework for diagnosing complexity in doped Clifford circuits and deepen our understanding of resource theories in multiqudit systems.

Classical spin liquids from frustrated Ising models in hyperbolic space

Authors: Fabian Köhler, Johanna Erdmenger, Roderich Moessner, Matthias Vojta

arXiv ID: 2506.02113 | Date: 2025-06-02

Abstract: Antiferromagnetic Ising models on frustrated lattices can realize classical spin liquids, with highly degenerate ground states and, possibly, fractionalized excitations and emergent gauge fields. Motivated by the recent interest in many-body system in negatively curved space, we study hyperbolic frustrated Ising models. Specifically, we consider nearest-neighbor Ising models on tesselations with odd-length loops in two-dimensional hyperbolic space. For finite systems with open boundaries we determine the ground-state degeneracy exactly, and we perform extensive finite-temperature Monte-Carlo simulations to obtain thermodynamic data as well as correlation functions. We show that the shape of the boundary, constituting an extensive part of the system, can be used to control low-energy states: Depending on the boundary, we find ordered or disordered ground states. Our results demonstrate how geometric frustration acts in curved space to produce classical spin liquids.

Learning Circuits with Infinite Tensor Networks

Authors: Joe Gibbs, Lukasz Cincio

arXiv ID: 2506.02105 | Date: 2025-06-02

Abstract: Hamiltonian simulation on quantum computers is strongly constrained by gate counts, motivating techniques to reduce circuit depths. While tensor networks are natural competitors to quantum computers, we instead leverage them to support circuit design, with datasets of tensor networks enabling a unitary synthesis inspired by quantum machine learning. For a target simulation in the thermodynamic limit, translation invariance is exploited to significantly reduce the optimization complexity, avoiding a scaling with system size. Our approach finds circuits to efficiently prepare ground states, and perform time evolution on both infinite and finite systems with substantially lower gate depths than conventional Trotterized methods. In addition to reducing CNOT depths, we motivate similar utility for fault-tolerant quantum algorithms, with a demonstrated 5.2×5.2\times reduction in TT-count to realize eiHte^{-iHt}. The key output of our approach is the optimized unit-cell of a translation invariant circuit. This provides an advantage for Hamiltonian simulation of finite, yet arbitrarily large, systems on real quantum computers.

The Motzkin Spaghetto

Authors: Zhao Zhang, Olai B. Mykland

arXiv ID: 2506.02103 | Date: 2025-06-02

Abstract: While highly entangled ground states of gapless local Hamiltonians have been known to exist in one dimension, their two-dimensional counterparts were only recently found, with rather sophisticated interactions involving at least four neighboring degrees of freedom. Here, we show that similar bipartite entanglement properties can be realized on a square lattice with anisotropic interactions in four different quadrants. The interaction to generate such entanglement is much simpler than the previous constructions by coupling orthogonal arrays of highly entangled chains. The new construction exhibits an entanglement phase transition with different scalings of entanglement entropy at the critical point and in the lowly entangled phase, and faster decay of the spectral gap in the highly entangled phase. The tensor network representation of the new ground state consists of tensors with lower rank, while preserving a global geometry similar to that of the original networks.

Magnetic correlations in the SU(3)SU(3) triangular-lattice tt-JJ model at finite doping

Authors: Annika Böhler, Fabian Grusdt, Annabelle Bohrdt

arXiv ID: 2506.01915 | Date: 2025-06-02

Abstract: Quantum simulation platforms have become powerful tools for investigating strongly correlated systems beyond the capabilities of classical computation. Ultracold alkaline-earth atoms and molecules now enable experimental realizations of SU(N)-symmetric Fermi-Hubbard models, yet theoretical understanding of these systems, particularly at finite doping remains limited. Here we investigate the strong-coupling limit of the SU(3)SU(3) symmetric Fermi-Hubbard model on the triangular lattice with dimensions up to 9×99\times9 lattice sites across the full doping range. Using a three-flavor extension of Gutzwiller-projected hidden fermion determinant states (G-HFDS), a neural network based variational ansatz, we analyze two- and three-point spin-spin and spin-spin-hole correlations of the SU(3)SU(3) Cartan generators. We further study binding energies for large periodic systems, and compare our results to the paradigmatic SU(2)SU(2) square lattice equivalent, finding strikingly similar magnetic correlations, but enhanced binding energies. Our results provide a foundation for future exploration of doped SU(N) Mott insulators, providing valuable insights for both theoretical developments and quantum simulation experiments.

Probing Quantum Spin Systems with Kolmogorov-Arnold Neural Network Quantum States

Authors: Mahmud Ashraf Shamim, Eric A F Reinhardt, Talal Ahmed Chowdhury, Sergei Gleyzer, Paulo T Araujo

arXiv ID: 2506.01891 | Date: 2025-06-02

Abstract: Neural Quantum States (NQS) are a class of variational wave functions parametrized by neural networks (NNs) to study quantum many-body systems. In this work, we propose \texttt{SineKAN}, a NQS \textit{ansatz} based on Kolmogorov-Arnold Networks (KANs), to represent quantum mechanical wave functions as nested univariate functions. We show that \texttt{SineKAN} wavefunction with learnable sinusoidal activation functions can capture the ground state energies, fidelities and various correlation functions of the one dimensional Transverse-Field Ising model, Anisotropic Heisenberg model, and Antiferromagnetic J1J2J_{1}-J_{2} model with different chain lengths. In our study of the J1J2J_1-J_2 model with L=100L=100 sites, we find that the \texttt{SineKAN} model outperforms several previously explored neural quantum state \textit{ansätze}, including Restricted Boltzmann Machines (RBMs), Long Short-Term Memory models (LSTMs), and Multi-layer Perceptrons (MLP) \textit{a.k.a.} Feed Forward Neural Networks, when compared to the results obtained from the Density Matrix Renormalization Group (DMRG) algorithm. We find that \texttt{SineKAN} models can be trained to high precisions and accuracies with minimal computational costs.

Observation of a Fault Tolerance Threshold with Concatenated Codes

Authors: Grace M. Sommers, Michael Foss-Feig, David Hayes, David A. Huse, Michael J. Gullans

arXiv ID: 2506.00579 | Date: 2025-05-31

Abstract: We introduce a fault-tolerant protocol for code concatenation of a generalized Shor code using a butterfly network architecture with high noise thresholds and low ancilla overhead to allow implementation on current devices. We develop a probability passing decoder using tensor networks that applies Bayesian updates to the marginal error probabilities after each layer of checks, achieving a state preparation threshold of ec0.089e_c \approx 0.089 for erasure errors, and 0.015\approx 0.015 for unheralded noise. We implement our state preparation protocol on ion-trap hardware with added noise to demonstrate the threshold behavior in a real quantum device. We further theoretically test the performance of our scheme as a quantum memory and for universal quantum computation through the preparation of low-noise magic states for state distillation and TT-gate injection.

Fermionic Magic Resources of Quantum Many-Body Systems

Authors: Piotr Sierant, Paolo Stornati, Xhek Turkeshi

arXiv ID: 2506.00116 | Date: 2025-05-30

Abstract: Understanding the computational complexity of quantum states is a central challenge in quantum many-body physics. In qubit systems, fermionic Gaussian states can be efficiently simulated on classical computers and hence can be employed as a natural baseline for evaluating quantum complexity. In this work, we develop a framework for quantifying fermionic magic resources, also referred to as fermionic non-Gaussianity, which constitutes an essential resource for universal quantum computation. We leverage the algebraic structure of the fermionic commutant to define the fermionic antiflatness (FAF)-an efficiently computable and experimentally accessible measure of non-Gaussianity, with a clear physical interpretation in terms of Majorana fermion correlation functions. Studying systems in equilibrium, we show that FAF detects phase transitions, reveals universal features of critical points, and uncovers special solvable points in many-body systems. Extending the analysis to out-of-equilibrium settings, we demonstrate that fermionic magic resources become more abundant in highly excited eigenstates of many-body systems. We further investigate the growth and saturation of FAF under ergodic many-body dynamics, highlighting the roles of conservation laws and locality in constraining the increase of non-Gaussianity during unitary evolution. This work provides a framework for probing quantum many-body complexity from the perspective of fermionic Gaussian states and opens up new directions for investigating fermionic magic resources in many-body systems. Our results establish fermionic non-Gaussianity, alongside entanglement and non-stabilizerness, as a resource relevant not only to foundational studies but also to experimental platforms aiming to achieve quantum advantage.

Tensor Network for Anomaly Detection in the Latent Space of Proton Collision Events at the LHC

Authors: Ema Puljak, Maurizio Pierini, Artur Garcia-Saez

arXiv ID: 2506.00102 | Date: 2025-05-30

Abstract: The pursuit of discovering new phenomena at the Large Hadron Collider (LHC) demands constant innovation in algorithms and technologies. Tensor networks are mathematical models on the intersection of classical and quantum machine learning, which present a promising and efficient alternative for tackling these challenges. In this work, we propose a tensor network-based strategy for anomaly detection at the LHC and demonstrate its superior performance in identifying new phenomena compared to established quantum methods. Our model is a parametrized Matrix Product State with an isometric feature map, processing a latent representation of simulated LHC data generated by an autoencoder. Our results highlight the potential of tensor networks to enhance new-physics discovery.

Instantons and topological order in two-leg electron ladders: A universality class

Authors: S. -R. Eric Yang, Hyun Cheol Lee, Hoang-Anh Le, In-Hwan Lee

arXiv ID: 2505.24130 | Date: 2025-05-30

Abstract: Our numerical study of the disordered Hubbard model with nearest-neighbor hopping shows that a two-leg electron ladder has a finite topological entanglement entropy in the regime where the density of states exhibits an exponentially decaying gap. The value of the topological entanglement entropy suggests that two-leg ladders belong to the same universality class as graphene zigzag nanoribbons, despite several structural differences. A Shankar-Witten-type bosonization Lagrangian with disorder captures several features of the numerically obtained results for disordered two-leg ladders. Additionally, we propose a Lagrangian in which the fusion of two semions residing on different chains generates a fermion (instanton). We apply this Lagrangian within the framework of the pinned charge-density-wave model and compute the relevant Green's function using the bosonization method. This approach predicts a linear density of states at a critical disorder strength. Below this threshold, a soft gap emerges, which is in qualitative agreement with our numerical results.

Domain-Aware Tensor Network Structure Search

Authors: Giorgos Iacovides, Wuyang Zhou, Chao Li, Qibin Zhao, Danilo Mandic

arXiv ID: 2505.23537 | Date: 2025-05-29

Abstract: Tensor networks (TNs) provide efficient representations of high-dimensional data, yet identification of the optimal TN structures, the so called tensor network structure search (TN-SS) problem, remains a challenge. Current state-of-the-art (SOTA) algorithms solve TN-SS as a purely numerical optimization problem and require extensive function evaluations, which is prohibitive for real-world applications. In addition, existing methods ignore the valuable domain information inherent in real-world tensor data and lack transparency in their identified TN structures. To this end, we propose a novel TN-SS framework, termed the tnLLM, which incorporates domain information about the data and harnesses the reasoning capabilities of large language models (LLMs) to directly predict suitable TN structures. The proposed framework involves a domain-aware prompting pipeline which instructs the LLM to infer suitable TN structures based on the real-world relationships between tensor modes. In this way, our approach is capable of not only iteratively optimizing the objective function, but also generating domain-aware explanations for the identified structures. Experimental results demonstrate that tnLLM achieves comparable TN-SS objective function values with much fewer function evaluations compared to SOTA algorithms. Furthermore, we demonstrate that the LLM-enabled domain information can be used to find good initializations in the search space for sampling-based SOTA methods to accelerate their convergence while preserving theoretical performance guarantees.

Dominant Kitaev interaction and field-induced quantum phase transitions in triangular-lattice KCeSe2

Authors: Mingtai Xie, Zheng Zhang, Weizhen Zhuo, Wei Xu, Jinfeng Zhu, Jan Embs, Lei Wang, Zikang Li, Huanpeng Bu, Anmin Zhang, Feng Jin, Jianting Ji, Zhongwen Ouyang, Liusuo Wu, Jie Ma, Qingming Zhang

arXiv ID: 2505.23502 | Date: 2025-05-29

Abstract: Realizing Kitaev interactions on triangular lattices offers a compelling platform for exploring quantum-spin-liquid physics beyond the conventional honeycomb lattice framework. Here, we investigate the triangular-lattice antiferromagnet KCeSe2, where multiple probes reveal strong magnetic anisotropy suggesting significant Kitaev physics. Through detailed and combined analysis of magnetization, neutron scattering, and thermodynamic experiments, we identify dominant ferromagnetic Kitaev (K=1.82K = -1.82 K) and antiferromagnetic Heisenberg (J=1.34J = 1.34 K) interactions that stabilize a stripe-yzyz ordered ground state via an order-by-disorder mechanism. Magnetic fields applied along the Kitaev bond direction induce two phase transitions at 1.67 T and 3.8 T, consistent with density matrix renormalization group (DMRG) calculations predictions of a progression from stripe-yzyz to stripe-canted and spin-polarized phases. Near the 1.67 T quantum critical point, enhanced quantum fluctuations suggest conditions favorable for exotic excitations. These results establish KCeSe2 as a platform for exploring Kitaev physics on triangular lattices.

An additive two-level parallel variant of the DMRG algorithm with coarse-space correction

Authors: Laura Grigori, Muhammad Hassan

arXiv ID: 2505.23429 | Date: 2025-05-29

Abstract: The density matrix renormalization group (DMRG) algorithm is a popular alternating minimization scheme for solving high-dimensional optimization problems in the tensor train format. Classical DMRG, however, is based on sequential minimization, which raises challenges in its implementation on parallel computing architectures. To overcome this, we propose a novel additive two-level DMRG algorithm that combines independent, local minimization steps with a global update step using a subsequent coarse-space minimization. Our proposed algorithm, which is directly inspired by additive Schwarz methods from the domain decomposition literature, is particularly amenable to implementation on parallel, distributed architectures since both the local minimization steps and the construction of the coarse-space can be performed in parallel. Numerical experiments on strongly correlated molecular systems demonstrate that the method achieves competitive convergence rates while achieving significant parallel speedups.

A New Scaling Function for QAOA Tensor Network Simulations

Authors: Goro Miki, Yasuhiro Tokura

arXiv ID: 2505.23256 | Date: 2025-05-29

Abstract: With the rapid development of quantum computers in recent years, the importance of performance evaluation in quantum algorithms has been increasing. One method that has gained attention for performing this evaluation on classical computers is tensor networks. Tensor networks not only reduce the computational cost required for simulations by using approximations but are also deeply connected to entanglement. Entanglement is one of the most important elements for the quantum advantages of quantum algorithms, but the direct relationship between quantum advantages and entanglement remains largely unexplored. Tensor networks are promising as a means to address this question. In this study, we focus on the entanglement in the Quantum Approximate Optimization Algorithm (QAOA). This study aims to investigate entanglement in QAOA by examining the relationship between the approximation rates of tensor networks and the performance of QAOA. Specifically, we actually perform tensor network simulations of QAOA on a classical computer and extend the study of the scaling relations presented in previous research. We have discovered that scaling relations hold even when entanglement entropy is used as the vertical axis. Furthermore, by analyzing the results of the numerical calculations, we propose a new function for the scaling relation. Additionally, we discovered interesting relationships regarding the behavior of entanglement in QAOA during our analysis. This research is expected to provide new insights into the theoretical foundation of the scaling relations presented in previous studies.

Emergent Quasiparticles \& Field-Tuned RIXS Spectra in a Trimerized Spin-1/2 Chain

Authors: Subhajyoti Pal, Pradeep Thakur, Ashis Kumar Nandy, Anamitra Mukherjee

arXiv ID: 2505.23208 | Date: 2025-05-29

Abstract: We investigate spin-flip excitations in the spin-1/2 trimer chain Cu3(P2O6OH)2\rm{Cu_3(P_2O_6OH)_2}, featuring an antiferromagnetic exchange motif J1J_1-J1J_1-J2J_2 with J1<J2J_1 < J_2. Using density matrix renormalization group (DMRG) simulations, we demonstrate that single-spin-flip processes induced by resonant inelastic X-ray scattering (RIXS) generate emergent gapless modes governed by the underlying trimer periodicity alongside distinct high-energy excitations. By combining exact diagonalization and real-space renormalization group (RG) techniques, we attribute these features to fractionalized spinons and composite quasiparticles arising from one- and two-trimer excitations. Furthermore, we show that multi-spin RIXS excitations yield experimentally distinguishable spectral signatures of composite modes absent in single-spin-flip spectra. At the field-induced 1/3 magnetization plateau, single-spin-flip RIXS spectra evolves with the magnetic field to favor spin-polarized composite quasiparticles. This trend culminates in a gapless spectrum of spin-1 excitations beyond the plateau, paving the way for field-tuned Bose condensation of composite modes.

Beyond mean-field dynamics of the Dicke model with non-Markovian dephasing

Authors: Anqi Mu, Nathan Ng, Andrew J. Millis, David R. Reichman

arXiv ID: 2505.23028 | Date: 2025-05-29

Abstract: We present a density matrix-based time dependent projection operator formalism to calculate the beyond mean-field dynamics of systems with non-Markovian local baths and one-to-all interactions. Such models encapsulate the physics of condensed phase systems immersed in optical cavities. We use this method, combined with tensor network influence functionals, to study the dynamics of the Dicke model coupled to non-Markovian local dephasing baths at zero temperature, which has a superradiant phase transition in the mean-field limit. The method corrects a spurious initial state dependence found in the mean-field dynamics and describes the emergence of new time scales which are absent in the mean-field dynamics. Our formalism, based on density matrices, is applicable to other quantum optical systems with one-to-all interactions at finite temperatures.

Roughening and dynamics of an electric flux string in a (2+1)D lattice gauge theory

Authors: Francesco Di Marcantonio, Sunny Pradhan, Sofia Vallecorsa, Mari Carmen Bañuls, Enrique Rico Ortega

arXiv ID: 2505.23853 | Date: 2025-05-29

Abstract: We investigate the roughening transition in the pure Z2\mathbb{Z}_2 lattice gauge theory in (2+1) dimensions. Using numerical simulations with matrix product states, we explore the static and dynamical properties of an electric flux string between two static charges as the coupling is varied and approaches the deconfinement phase transition from the confined phase. Within the roughening region, we obtain the universal Lüscher correction to the confining potential and observe the expected restoration of rotational symmetry. Our simulations of the out-of-equilibrium evolution of a string reveal that the growth of the entanglement entropy of the state and the string width exhibit qualitatively different behavior in the roughening region compared to the deeply confined one. In particular, we find that the rate of entropy growth is consistent with an effective description of the string excitations by a bosonic model in the roughening phase.

Optimizing QUBO on a quantum computer by mimicking imaginary time evolution

Authors: Yahui Chai, Alice Di Tucci

arXiv ID: 2505.22924 | Date: 2025-05-28

Abstract: We propose a hybrid quantum-classical algorithm for solving QUBO problems using an Imaginary Time Evolution-Mimicking Circuit (ITEMC). The circuit parameters are optimized to closely mimic imaginary time evolution, using only single- and two-qubit expectation values. This significantly reduces the measurement overhead by avoiding full energy evaluation. By updating the initial state based on results from last step iteratively, the algorithm quickly converges to the low-energy solutions. With a pre-sorting step that optimizes quantum gate ordering based on QUBO coefficients, the convergence is further improved. Our classical simulations achieve approximation ratios above 0.99 up to 150 qubits. Furthermore, the linear scaling of entanglement entropy with system size suggests that the circuit is challenging to simulate classically using tensor networks. We also demonstrate hardware runs on IBM's device for 40, 60, and 80 qubits, and obtain solutions compatible with that from simulated annealing.

Flow to Nishimori universality in weakly monitored quantum circuits with qubit loss

Authors: Malte Pütz, Romain Vasseur, Andreas W. W. Ludwig, Simon Trebst, Guo-Yi Zhu

arXiv ID: 2505.22720 | Date: 2025-05-28

Abstract: In circuit-based quantum state preparation, qubit loss and coherent errors are circuit imperfections that imperil the formation of long-range entanglement beyond a certain threshold. The critical theory at the threshold is a continuous entanglement transition known to be described by a (2+0)-dimensional non-unitary conformal field theory which, for the two types of imperfections of certain circuits, is described by either percolation or Nishimori criticality, respectively. Here we study the threshold behavior when the two types of errors simultaneously occur and show that, when moving away from the Clifford-regime of projective stabilizer measurements, the percolation critical point becomes unstable and the critical theory flows to Nishimori universality. We track this critical renormalization group (RG) crossover flow by mapping out the entanglement phase diagrams, parametrized by the probability and strength of random weak measurements, of two dual protocols preparing surface code or GHZ-class cat states from a parent cluster state via constant-depth circuits. Extensive numerical simulations, using hybrid Gaussian fermion and tensor network / Monte Carlo sampling techniques on systems with more than a million qubits, demonstrate that an infinitesimal deviation from the Clifford regime leads to a sudden, strongly non-monotonic entanglement growth at the incipient non-unitary RG flow. We argue that spectra of scaling dimensions of both the percolation and Nishimori fixed points exhibit multifractality. For percolation, we provide the exact (non-quadratic) multifractal spectrum of exponents, while for the Nishimori fixed point we show high-precision numerical results for five leading exponents characterizing multifractality.

Subsystem Symmetry-Protected Topological Phases from Subsystem SymTFT of 2-Foliated Exotic Tensor Gauge Theory

Authors: Qiang Jia, Zhian Jia

arXiv ID: 2505.22261 | Date: 2025-05-28

Abstract: Symmetry topological field theory (SymTFT), or topological holography, posits a correspondence between symmetries in a dd-dimensional theory and topological order in a (d+1)(d+1)-dimensional theory. In this work, we extend this framework to subsystem symmetries and develop subsystem SymTFT as a systematic tool to characterize and classify subsystem symmetry-protected topological (SSPT) phases. For (2+1)(2+1)D gapped phases, we introduce a 2-foliated (3+1)(3+1)D exotic tensor gauge theory (which is equivalent to 2-foliated (3+1)(3+1)D BF theory via exotic duality) as the subsystem SymTFT and systematically analyze its topological boundary conditions and linearly rigid subsystem symmetries. Taking subsystem symmetry groups G=ZNG = \mathbb{Z}_N and G=ZN×ZMG=\mathbb{Z}_N \times \mathbb{Z}_M as examples, we demonstrate how to recover the classification scheme C[G]=H2(G×2,U(1))/(H2(G,U(1)))3\mathcal{C}[G] = H^{2}(G^{\times 2}, U(1)) / \left( H^2(G, U(1)) \right)^3, which was previously derived by examining topological invariant under linear subsystem-symmetric local unitary transformations in the lattice Hamiltonian formalism. To illustrate the correspondence between field-theoretic and lattice descriptions, we further analyze Z2×Z2\mathbb{Z}_2 \times \mathbb{Z}_2 and ZN×ZM\mathbb{Z}_N \times \mathbb{Z}_M cluster state models as concrete examples.

Breaking the Curse of Dimensionality: Solving Configurational Integrals for Crystalline Solids by Tensor Networks

Authors: Duc P. Truong, Benjamin Nebgen, Derek DeSantis, Dimiter N. Petsev, Kim Ø. Rasmussen, Boian S. Alexandrov

arXiv ID: 2505.21826 | Date: 2025-05-27

Abstract: Accurately evaluating configurational integrals for dense solids remains a central and difficult challenge in the statistical mechanics of condensed systems. Here, we present a novel tensor network approach that reformulates the high-dimensional configurational integral for identical-particle crystals into a sequence of computationally efficient summations. We represent the integrand as a high-dimensional tensor and apply tensor-train (TT) decomposition together with a custom TT-cross interpolation scheme. This approach avoids the need to explicitly construct the full tensor, which would otherwise be computationally intractable. We introduce tailored rank-1 and rank-2 schemes optimized for sharply peaked Boltzmann probability densities, typical in crystalline solids. When applied to the calculation of internal energy and pressure-temperature curves for crystalline copper (Cu) and argon (Ar), as well as the alpha-to-beta phase transition in tin (Sn), our method accurately reproduces molecular dynamics simulation results using tight-binding, machine learning (HIP-NN), and MEAM potentials, all within seconds of computation time.

LaX: Boosting Low-Rank Training of Foundation Models via Latent Crossing

Authors: Ruijie Zhang, Ziyue Liu, Zhengyang Wang, Zheng Zhang

arXiv ID: 2505.21732 | Date: 2025-05-27

Abstract: Training foundation models such as ViTs and LLMs requires tremendous computing cost. Low-rank matrix or tensor factorization offers a parameter-efficient alternative, but often downgrades performance due to the restricted parameter space. In this work, we introduce {\textbf{Latent Crossing (LaX)}} -- a simple yet effective plug-and-play module that enhances the capacity of low-rank models by enabling information flow across low-rank subspaces. We extensively validate the benefits of LaX on pre-training tasks with ViT-Base/Large and LLaMA-like models ranging from 60M to 1B parameters. LaX boosts low-rank model performance to match or exceed the full-rank baselines while using 2-3\(\times\) fewer parameters. When equipped with low-rank adapters (i.e., LoRA) for fine-tuning LLaMA-7/13B, LaX consistently improves performance on arithmetic and common sense reasoning tasks with negligible cost.

Pair binding and Hund's rule breaking in high-symmetry fullerenes

Authors: R. Rausch, C. Karrasch

arXiv ID: 2505.21455 | Date: 2025-05-27

Abstract: Highly-symmetric molecules often exhibit degenerate tight-binding states at the Fermi edge. This typically results in a magnetic ground state if small interactions are introduced in accordance with Hund's rule. In some cases, Hund's rule may be broken, which signals pair binding and goes hand-in-hand with an attractive pair-binding energy. We investigate pair binding and Hund's rule breaking for the Hubbard model on high-symmetry fullerenes C20_{20}, C28_{28}, C40_{40}, and C60_{60} by using large-scale density-matrix renormalization group calculations. We exploit the SU(2) spin symmetry, the U(1) charge symmetry, and optionally the Z(N) spatial rotation symmetry of the problem. For C20_{20}, our results agree well with available exact-diagonalization data, but our approach is numerically much cheaper. We find a Mott transition at Uc2.2tU_c\sim2.2t, which is much smaller than the previously reported value of Uc4.1tU_c\sim4.1t that was extrapolated from a few datapoints. We compute the pair-binding energy for arbitrary values of UU and observe that it remains overall repulsive. For larger fullerenes, we are not able to evaluate the pair binding energy with sufficient precision, but we can still investigate Hund's rule breaking. For C28_{28}, we find that Hund's rule is fulfilled with a magnetic spin-2 ground state that transitions to a spin-1 state at Uc,15.4tU_{c,1}\sim5.4t before the eventual Mott transition to a spin singlet takes place at Uc,211.6tU_{c,2}\sim 11.6t. For C40_{40}, Hund's rule is broken in the singlet ground state, but is restored if the system is doped with one electron. Hund's rule is also broken for C60_{60}, and the doping with two or three electrons results in a minimum-spin state. Our results are consistent with an electronic mechanism of superconductivity for C60_{60} lattices. We speculate that the high geometric frustration of small fullerenes is detrimental to pair binding.

Reduced Density Matrices and Phase-Space Distributions in Thermofield Dynamics

Authors: Bartosz Błasiak, Dominik Brey, Rocco Martinazzo, Irene Burghardt

arXiv ID: 2505.21302 | Date: 2025-05-27

Abstract: Thermofield dynamics (TFD) is a powerful framework to account for thermal effects in a wavefunction setting, and has been extensively used in physics and quantum optics. TFD relies on a duplicated state space and creates a correlated two-mode thermal state via a Bogoliubov transformation acting on the vacuum state. However, a very useful variant of TFD uses the vacuum state as initial condition and transfers the Bogoliubov transformation into the propagator. This variant, referred to here as the inverse Bogoliubov transformation (iBT) variant, has recently been applied to vibronic coupling problems and coupled-oscillator Hamiltonians in a chemistry context, where the method is combined with efficient tensor network methods for high-dimensional quantum propagation. In the iBT/TFD representation, the mode expectation values are clearly defined and easy to calculate, but the thermalized reduced particle distributions such as the reduced 1-particle densities or Wigner distributions are highly non-trivial due to the Bogoliubov back-transformation of the original thermal TFD wavefunction. Here we derive formal expressions for the reduced 1-particle density matrix (1-RDM) that uses the correlations between the real and tilde modes encoded in the associated reduced 2-particle density matrix (2-RDM). We apply this formalism to define the 1-RDM and the Wigner distributions in the special case of a thermal harmonic oscillator. Moreover, we discuss several approximate schemes that can be extended to higher-dimensional distributions. These methods are demonstrated for the thermal reduced 1-particle density of an anharmonic oscillator.

Scalable Quantum Algorithm for Meson Scattering in a Lattice Gauge Theory

Authors: Yahui Chai, Yibin Guo, Stefan Kühn

arXiv ID: 2505.21240 | Date: 2025-05-27

Abstract: Scattering processes are fundamental for understanding the structure of matter, yet simulating their real-time dynamics remains challenging for classical computers. Quantum computing and quantum-inspired methods offer a promising avenue for efficiently simulating such phenomena. In this work, we investigate meson scattering in a (1+1)-dimensional Z2 lattice gauge theory with staggered fermions. We develop a quantum subspace expansion technique to construct high-fidelity meson creation operators across a broad range of masses and momenta. Using Tensor Networks simulations, we study both elastic and inelastic scattering and provide a detailed analysis of energy transfer, entanglement entropy, and new particle production during the dynamics. In addition, we design an efficient quantum circuit for meson wave packet preparation using Givens rotations, significantly reducing the circuit depth compared to existing methods. Our work provides a non-variational and scalable framework for simulating meson scattering on near-term quantum devices, and provides a concrete strategy for quantum simulation to analyze non-perturbative dynamical processes in confining gauge theories.

Scalable Quantum Algorithm for Meson Scattering in a Lattice Gauge Theory

Authors: Yahui Chai, Yibin Guo, Stefan Kühn

arXiv ID: 2505.21240 | Date: 2025-05-27

Abstract: Scattering processes are fundamental for understanding the structure of matter, yet simulating their real-time dynamics remains challenging for classical computers. Quantum computing and quantum-inspired methods offer a promising avenue for efficiently simulating such phenomena. In this work, we investigate meson scattering in a (1+1)-dimensional Z2 lattice gauge theory with staggered fermions. We develop a quantum subspace expansion technique to construct high-fidelity meson creation operators across a broad range of masses and momenta. Using Tensor Networks simulations, we study both elastic and inelastic scattering and provide a detailed analysis of energy transfer, entanglement entropy, and new particle production during the dynamics. In addition, we design an efficient quantum circuit for meson wave packet preparation using Givens rotations, significantly reducing the circuit depth compared to existing methods. Our work provides a non-variational and scalable framework for simulating meson scattering on near-term quantum devices, and provides a concrete strategy for quantum simulation to analyze non-perturbative dynamical processes in confining gauge theories.

Ginsparg-Wilson Hamiltonians with Improved Chiral Symmetry

Authors: Hersh Singh

arXiv ID: 2505.20419 | Date: 2025-05-26

Abstract: We construct a family of Ginsparg-Wilson Hamiltonians with improved chiral properties, starting from a construction of Creutz-Horvath-Neuberger that provides a doubler-free Hamiltonian lattice regularization for Dirac fermions in even spacetime dimensions. We use a higher-order generalization of the Ginsparg-Wilson relation due to Fujikawa, which yields an order-kk Hamiltonian overlap operator for each integer k0k \geq 0, with an exactly conserved but nonquantized chiral charge that becomes quantized as kk \to \infty. Our construction provides physical insight into how Fujikawa's higher-order Ginsparg-Wilson relation improves chiral symmetry while reproducing the anomaly, highlighting the trade-offs inherent in any Hamiltonian lattice realization of an anomalous chiral symmetry. This class of Hamiltonian lattice regularizations, with their tunable chiral symmetry properties, offers potential advantages for quantum and tensor-network simulations.

Quantum computation of hadron scattering in a lattice gauge theory

Authors: Zohreh Davoudi, Chung-Chun Hsieh, Saurabh V. Kadam

arXiv ID: 2505.20408 | Date: 2025-05-26

Abstract: We present a digital quantum computation of two-hadron scattering in a Z2Z_2 lattice gauge theory in 1+1 dimensions. We prepare well-separated single-particle wave packets with desired momentum-space wavefunctions, and simulate their collision through digitized time evolution. Multiple hadronic wave packets can be produced using the efficient, systematically improvable algorithm of this work, achieving high fidelity with the target initial state. Specifically, employing a trapped-ion quantum computer (IonQ Forte), we prepare up to three meson wave packets using 11 and 27 system qubits, and simulate collision dynamics of two meson wave packets for the smaller system. Results for local observables are consistent with numerical simulations at early times, but decoherence effects limit evolution into long times. We demonstrate the critical role of high-fidelity initial states for precision measurements of state-sensitive observables, such as SS-matrix elements. Our work establishes the potential of quantum computers in simulating hadron-scattering processes in strongly interacting gauge theories.

It from ETH: Multi-interval Entanglement and Replica Wormholes from Large-cc BCFT Ensemble

Authors: Hao Geng, Ling-Yan Hung, Yikun Jiang

arXiv ID: 2505.20385 | Date: 2025-05-26

Abstract: We provide a derivation of the Ryu-Takayanagi (RT) formula in 3D gravity for generic boundary subregion--including RT surface phase transitions--directly from the dual two-dimensional conformal field theory (CFT). Our approach relies on the universal statistics of the algebraic conformal data and the large-cc behavior of conformal blocks with Cardy boundaries involved. We observe the emergence of 3D multi-boundary black holes with Karch-Randall branes from entangled states of any number of CFT's with and without Cardy boundaries. The RT formula is obtained directly from the CFT in the high-temperature regime. Two direct applications are: 1)\textbf{1)} A simple derivation of the multi-interval entanglement entropy for the vacuum state of a single CFT; 2)\textbf{2)} A CFT-based detection of the emergence of replica wormholes in the context of entanglement islands and black hole microstate counting. Our framework yields the first holographic random tensor network that faithfully captures the entanglement structure of holographic CFTs. These results imply that bulk spacetime geometries indeed emerge from the eigenstate thermalization hypothesis (ETH) in the dual field theory in the large-cc limi--a paradigm we refer to as It from ETH\textit{It from ETH}.

Observation of hadron scattering in a lattice gauge theory on a quantum computer

Authors: Julian Schuhmacher, Guo-Xian Su, Jesse J. Osborne, Anthony Gandon, Jad C. Halimeh, Ivano Tavernelli

arXiv ID: 2505.20387 | Date: 2025-05-26

Abstract: Scattering experiments are at the heart of high-energy physics (HEP), breaking matter down to its fundamental constituents, probing its formation, and providing deep insight into the inner workings of nature. In the current huge drive to forge quantum computers into complementary venues that are ideally suited to capture snapshots of far-from-equilibrium HEP dynamics, a major goal is to utilize these devices for scattering experiments. A major obstacle in this endeavor has been the hardware overhead required to access the late-time post-collision dynamics while implementing the underlying gauge symmetry. Here, we report on the first quantum simulation of scattering in a lattice gauge theory (LGT), performed on \texttt{IBM}'s \texttt{ibm\_marrakesh} quantum computer. Specifically, we quantum-simulate the collision dynamics of electrons and positrons as well as mesons in a U(1)\mathrm{U}(1) LGT representing 1+11+1D quantum electrodynamics (QED), uncovering rich post-collision dynamics that we can precisely tune with a topological ΘΘ-term and the fermionic mass. By monitoring the time evolution of the scattering processes, we are able to distinguish between two main regimes in the wake of the collision. The first is characterized by the delocalization of particles when the topological ΘΘ-term is weak, while the second regime shows localized particles with a clear signature when the ΘΘ-term is nontrivial. Furthermore, we show that by quenching to a small mass at the collision point, inelastic scattering occurs with a large production of matter reminiscent of quantum many-body scarring. Our work provides a major step forward in the utility of quantum computers for investigating the real-time quantum dynamics of HEP collisions.

Derivations for the MPS overlap formulas of rational spin chains

Authors: Tamas Gombor

arXiv ID: 2505.20234 | Date: 2025-05-26

Abstract: We derive a universal formula for the overlaps between integrable matrix product states (MPS) and Bethe eigenstates in glN\mathfrak{gl}_{N} symmetric spin chains. This formula expresses the normalized overlap as a product of a MPS-independent Gaudin-determinant ratio and a MPS-dependent scalar factor constructed from eigenvalues of commuting operators, defined via the KK-matrix associated with the MPS. Our proof is fully representation-independent and relies solely on algebraic Bethe Ansatz techniques and the KTKT-relation. We also propose a generalization of the overlap formula to soN\mathfrak{so}_{N} and spN\mathfrak{sp}_{N} spin chains, supported by algebra embeddings and low-rank isomorphisms. These results significantly broaden the class of integrable initial states for which exact overlap formulas are available, with implications for quantum quenches and defect CFTs.

Tensorization is a powerful but underexplored tool for compression and interpretability of neural networks

Authors: Safa Hamreras, Sukhbinder Singh, Román Orús

arXiv ID: 2505.20132 | Date: 2025-05-26

Abstract: Tensorizing a neural network involves reshaping some or all of its dense weight matrices into higher-order tensors and approximating them using low-rank tensor network decompositions. This technique has shown promise as a model compression strategy for large-scale neural networks. However, despite encouraging empirical results, tensorized neural networks (TNNs) remain underutilized in mainstream deep learning. In this position paper, we offer a perspective on both the potential and current limitations of TNNs. We argue that TNNs represent a powerful yet underexplored framework for deep learning--one that deserves greater attention from both engineering and theoretical communities. Beyond compression, we highlight the value of TNNs as a flexible class of architectures with distinctive scaling properties and increased interpretability. A central feature of TNNs is the presence of bond indices, which introduce new latent spaces not found in conventional networks. These internal representations may provide deeper insight into the evolution of features across layers, potentially advancing the goals of mechanistic interpretability. We conclude by outlining several key research directions aimed at overcoming the practical barriers to scaling and adopting TNNs in modern deep learning workflows.

Matrix-product-state approach for qubits-waveguide systems in real space

Authors: Shimpei Goto

arXiv ID: 2505.19424 | Date: 2025-05-26

Abstract: We present a matrix-product-state-based numerical approach for simulating systems composed of several qubits and a common one-dimensional waveguide. In the presented approach, the one-dimensional waveguide is modeled in real space. Thus, one can use the advantage of matrix-product states that are suited for simulating low-entangled one-dimensional systems. The price to pay is that the vacuum of the waveguide in this modeling becomes the Bogoliubov vacuum, and one has to consider a not-so-small local Hilbert space for bosonic degrees of freedom. To manage the large local Hilbert space, we adopt the recently proposed single-site schemes. We demonstrate the potential of the presented approach by simulating superradiant phenomena within the Hamiltonian dynamics.

Project For Advancement of Software Usability in Materials Science

Authors: Kazuyoshi Yoshimi, Yuichi Motoyama, Tatsumi Aoyama, Mitsuaki Kawamura, Naoki Kawashima

arXiv ID: 2505.18390 | Date: 2025-05-23

Abstract: The Institute for Solid State Physics (ISSP) at The University of Tokyo has been carrying out a software development project named ``the Project for Advancement of Software Usability in Materials Science (PASUMS)". Since the launch of PASUMS, various open-source software programs have been developed/advanced, including ab initio calculations, effective model solvers, and software for machine learning. We also focus on activities that make the software easier to use, such as developing comprehensive computing tools that enable efficient use of supercomputers and interoperability between different software programs. We hope to contribute broadly to developing the computational materials science community through these activities.

A tensor network approach for chaotic time series prediction

Authors: Rodrigo Martínez-Peña, Román Orús

arXiv ID: 2505.17740 | Date: 2025-05-23

Abstract: Making accurate predictions of chaotic time series is a complex challenge. Reservoir computing, a neuromorphic-inspired approach, has emerged as a powerful tool for this task. It exploits the memory and nonlinearity of dynamical systems without requiring extensive parameter tuning. However, selecting and optimizing reservoir architectures remains an open problem. Next-generation reservoir computing simplifies this problem by employing nonlinear vector autoregression based on truncated Volterra series, thereby reducing hyperparameter complexity. Nevertheless, the latter suffers from exponential parameter growth in terms of the maximum monomial degree. Tensor networks offer a promising solution to this issue by decomposing multidimensional arrays into low-dimensional structures, thus mitigating the curse of dimensionality. This paper explores the application of a previously proposed tensor network model for predicting chaotic time series, demonstrating its advantages in terms of accuracy and computational efficiency compared to conventional echo state networks. Using a state-of-the-art tensor network approach enables us to bridge the gap between the tensor network and reservoir computing communities, fostering advances in both fields.

Inchworm tensor train hybridization expansion quantum impurity solver

Authors: Yang Yu, André Erpenbeck, Dominika Zgid, Guy Cohen, Olivier Parcollet, Emanuel Gull

arXiv ID: 2505.16117 | Date: 2025-05-22

Abstract: The investigation of quantum impurity models plays a crucial role in condensed matter physics because of their wide-ranging applications, such as embedding theories and transport problems. Traditional methods often fall short of producing accurate results for multi-orbital systems with complex interactions and off-diagonal hybridizations. Recently, tensor-train-based integration and summation techniques have shown promise as effective alternatives. In this study, we use tensor train methods to tackle quantum impurity problems formulated within the imaginary-time inchworm hybridization expansion framework. We identify key challenges in the inchworm expansion itself and its interplay with tensor-train-based methods. We demonstrate the accuracy and versatility of our approach by solving general quantum impurity problems. Our results suggest that tensor-train decomposition schemes offer a viable path toward accurate and efficient multi-orbital impurity solvers.

Prethermalization, shadowing breakdown, and the absence of Trotterization transition in quantum circuits

Authors: Marko Znidaric

arXiv ID: 2505.15521 | Date: 2025-05-21

Abstract: One of premier utilities of present day noisy quantum computers is simulation of many-body quantum systems. We study how long in time is such a discrete-time simulation representative of a continuous time Hamiltonian evolution, namely, a finite time-step introduces so-called Trotterization errors. We show that the truncated operator propagator (Ruelle-Pollicott resonances) is a powerful tool to that end, as well as to study prethermalization and discrete time crystals, including finding those phenomena at large gate duration. We show that the effective energy is more stable than suggested by Trotter errors -- a manifestation of prethermalization -- while all other observables are not. Even the most stable observable though deteriorates in the thermodynamic limit. Different than in classical systems with the strongest chaos, where the faithfulness time (the shadowing time) can be infinite, in quantum many-body chaotic systems it is finite. A corollary of our results is also that, opposite to previous claims, there is no Trotterization transition in non-integrable many-body quantum systems. We demonstrate our results on a one-dimensional (1d) kicked Ising model, as well as on 1d kicked XX model and 2d kicked Ising model. The truncated propagator is also used to calculate the energy diffusion constant in the tilted-field Ising model with high accuracy.

Controlling quantum phases with electric fields in one-dimensional Hubbard systems

Authors: D. Arisa, R. M. Dos Santos, Isaac M. Carvalho, Vivian V. França

arXiv ID: 2505.15449 | Date: 2025-05-21

Abstract: Quantum systems under electric fields provide a powerful framework for uncovering and controlling novel quantum phases, especially in low-dimensional systems with strong correlations. In this work, we investigate quantum phase transitions induced by an electric potential difference in a one-dimensional half-filled Hubbard chain. By analyzing (i) tunneling and pairing mechanisms, (ii) charge and spin gaps, and (iii) entanglement between the chain halves, we identify three distinct phases: Mott insulator, metal and band-like insulator. The metallic regime, characterized by the closing of both charge and spin gaps, is accompanied by a field-dependent kinetic energy and a quasi-periodic oscillatory behavior of pairing response and entanglement. Although the metallic phase persists for different magnetizations, its extent in the phase diagram shrinks as spin polarization increases.

Saten: Sparse Augmented Tensor Networks for Post-Training Compression of Large Language Models

Authors: Ryan Solgi, Kai Zhen, Rupak Vignesh Swaminathan, Nathan Susanj, Athanasios Mouchtaris, Siegfried Kunzmann, Zheng Zhang

arXiv ID: 2505.14871 | Date: 2025-05-20

Abstract: The efficient implementation of large language models (LLMs) is crucial for deployment on resource-constrained devices. Low-rank tensor compression techniques, such as tensor-train (TT) networks, have been widely studied for over-parameterized neural networks. However, their applications to compress pre-trained large language models (LLMs) for downstream tasks (post-training) remains challenging due to the high-rank nature of pre-trained LLMs and the lack of access to pretraining data. In this study, we investigate low-rank tensorized LLMs during fine-tuning and propose sparse augmented tensor networks (Saten) to enhance their performance. The proposed Saten framework enables full model compression. Experimental results demonstrate that Saten enhances both accuracy and compression efficiency in tensorized language models, achieving state-of-the-art performance.

Multireference Embedding and Fragmentation Methods for Classical and Quantum Computers: from Model Systems to Realistic Applications

Authors: Shreya Verma, Abhishek Mitra, Qiaohong Wang, Ruhee D'Cunha, Bhavnesh Jangid, Matthew R. Hennefarth, Valay Agarawal, Leon Otis, Soumi Haldar, Matthew R. Hermes, Laura Gagliardi

arXiv ID: 2505.13394 | Date: 2025-05-19

Abstract: One of the primary challenges in quantum chemistry is the accurate modeling of strong electron correlation. While multireference methods effectively capture such correlation, their steep scaling with system size prohibits their application to large molecules and extended materials. Quantum embedding offers a promising solution by partitioning complex systems into manageable subsystems. In this review, we highlight recent advances in multireference density matrix embedding and localized active space self-consistent field approaches for complex molecules and extended materials. We discuss both classical implementations and the emerging potential of these methods on quantum computers. By extending classical embedding concepts to the quantum landscape, these algorithms have the potential to expand the reach of multireference methods in quantum chemistry and materials.

Verifying Quantum Memory in the Dynamics of Spin Boson Models

Authors: Charlotte Bäcker, Valentin Link, Walter T. Strunz

arXiv ID: 2505.13067 | Date: 2025-05-19

Abstract: We investigate the nature of memory effects in the non-Markovian dynamics of spin boson models. Local quantum memory criteria can be used to indicate that the reduced dynamics of an open system necessarily requires a quantum memory in its environment. We apply two such criteria, derived from different definitions put forward in the literature, to spin boson and two-spin boson models. For the computation of dynamical maps and process tensors, we employ a numerically exact method for non-Markovian open system dynamics based on matrix product operator influence functionals, that can be applied across broad parameter regimes. We find that, with access to single-intervention process tensors, one can generally predict quantum memory in the dynamics at low temperatures. Given instead only the dynamical map, we are still able to detect quantum memory in the case of resonant environments at short evolution times. Moreover, we confirm quantum memory in the stationary dynamical regime using process tensors with the correlated steady state of system and environment as initial condition.

Independent Set Enumeration in King Graphs by Tensor Network Contractions

Authors: Kai Liang

arXiv ID: 2505.12776 | Date: 2025-05-19

Abstract: This paper discusses the enumeration of independent sets in king graphs of size m×nm \times n, based on the tensor network contractions algorithm given in reference~\cite{tilEnum}. We transform the problem into Wang tiling enumeration within an (m+1)×(n+1)(m+1) \times (n+1) rectangle and compute the results for all cases where m+n79m + n \leq 79 using tensor network contraction algorithm, and provided an approximation for larger m,nm, n. Using the same algorithm, we also enumerated independent sets with vertex number restrictions. Based on the results, we analyzed the vertex number that maximize the enumeration for each pair (m,n)(m, n). Additionally, we compute the corresponding weighted enumeration, where each independent set is weighted by the number of its vertices (i.e., the total sum of vertices over all independent sets). The approximations for larger m,nm, n are given as well. Our results have added thousands of new items to the OEIS sequences A089980 and A193580. In addition, the combinatorial problems above are closely related to the hard-core model in physics. We estimate some important constants based on the existing results, and the relative error between our estimation of the entropy constant and the existing results is less than 10910^{-9}.

Exactly solvable many-body dynamics from space-time duality

Authors: Bruno Bertini, Pieter W. Claeys, Tomaž Prosen

arXiv ID: 2505.11489 | Date: 2025-05-16

Abstract: Recent years have seen significant advances, both theoretical and experimental, in our understanding of quantum many-body dynamics. Given this problem's high complexity, it is surprising that a substantial amount of this progress can be ascribed to exact analytical results. Here we review dual-unitary circuits as a particular setting leading to exact results in quantum many-body dynamics. Dual-unitary circuits constitute minimal models in which space and time are treated on an equal footings, yielding exactly solvable yet possibly chaotic evolution. They were the first in which current notions of quantum chaos could be analytically quantified, allow for a full characterisation of the dynamics of thermalisation, scrambling, and entanglement (among others), and can be experimentally realised in current quantum simulators. Dual-unitarity is a specific fruitful implementation of the more general idea of space-time duality in which the roles of space and time are exchanged to access relevant dynamical properties of quantum many-body systems.

TensorMixedStates: a Julia library for simulating pure and mixed quantum states using matrix product states

Authors: Jérôme Houdayer, Grégoire Misguich

arXiv ID: 2505.11377 | Date: 2025-05-16

Abstract: We introduce TensorMixedStates, a Julia library built on top of ITensor which allows the simulation of quantum systems in presence of dissipation using matrix product states (MPS). It offers three key features: i) it implements the MPS representation for mixed states along with associated operations, in particular the time evolution according to a Lindblad equation or discrete time evolution using non-unitary gates (quantum channels), ii) it is based on ITensor, which has proven its effectiveness and which gives access to efficient low-level tensor manipulation as well state-of-the-art algorithms (like DMRG, TDVP, quantum numbers conservation and automated parallelization), finally iii) it presents a user-friendly interface allowing writing sophisticated simulations for pure and mixed quantum states in a few lines of code.

Quantum data generation in a denoising model with multiscale entanglement renormalization network

Authors: Wei-Wei Zhang, Xiaopeng Huang, Shenglin Shan, Wei Zhao, Beiya Yang, Wei Pan, Haobin Shi

arXiv ID: 2505.10796 | Date: 2025-05-16

Abstract: Quantum technology has entered the era of noisy intermediate-scale quantum (NISQ) information processing. The technological revolution of machine learning represented by generative models heralds a great prospect of artificial intelligence, and the huge amount of data processes poses a big challenge to existing computers. The generation of large quantities of quantum data will be a challenge for quantum artificial intelligence. In this work, we present an efficient noise-resistant quantum data generation method that can be applied to various types of NISQ quantum processors, where the target quantum data belongs to a certain class and our proposal enables the generation of various quantum data belonging to the target class. Specifically, we propose a quantum denoising probability model (QDM) based on a multiscale entanglement renormalization network (MERA) for the generation of quantum data. To show the feasibility and practicality of our scheme, we demonstrate the generations of the classes of GHZ-like states and W-like states with a success rate above 99%. Our MREA QDM can also be used to denoise multiple types of quantum data simultaneously. We show the success rate of denoising both GHZ-like and W-like states with a single qubit noise environment of noise level within 1/4 can approximate to be 100%, and with two other types of noise environment with noise level within 1/4 can be above 90%. Our quantum data generation scheme provides new ideas and prospects for quantum generative models in the NISQ era.

Distributed Realization of Color Codes for Quantum Error Correction

Authors: Nitish Kumar Chandra, David Tipper, Reza Nejabati, Eneet Kaur, Kaushik P. Seshadreesan

arXiv ID: 2505.10693 | Date: 2025-05-15

Abstract: Color codes are a leading class of topological quantum error-correcting codes with modest error thresholds and structural compatibility with two-dimensional architectures, which make them well-suited for fault-tolerant quantum computing (FTQC). Here, we propose and analyze a distributed architecture for realizing the (6.6.6) color code. The architecture involves interconnecting patches of the color code housed in different quantum processing units (QPUs) via entangled pairs. To account for noisy interconnects, we model the qubits in the color code as being subject to a bit-flip noise channel, where the qubits on the boundary (seam) between patches experience elevated noise compared to those in the bulk. We investigate the error threshold of the distributed color code under such asymmetric noise conditions by employing two decoders: a tensor-network-based decoder and a recently introduced concatenated Minimum Weight Perfect Matching (MWPM) algorithm. Our simulations demonstrate that elevated noise on seam qubits leads to a slight reduction in threshold for the tensor-network decoder, whereas the concatenated MWPM decoder shows no significant change in the error threshold, underscoring its effectiveness under asymmetric noise conditions. Our findings thus highlight the robustness of color codes in distributed architectures and provide valuable insights into the practical realization of FTQC involving noisy interconnects between QPUs.

Exploring Variational Entanglement Hamiltonians

Authors: Yanick S. Kind, Benedikt Fauseweh

arXiv ID: 2505.10530 | Date: 2025-05-15

Abstract: Recent advances in analog and digital quantum-simulation platforms have enabled exploration of the spectrum of entanglement Hamiltonians via variational algorithms. In this work we analyze the convergence properties of the variationally obtained solutions and compare them to numerically exact calculations in quantum critical systems. We demonstrate that interpreting the cost functional as an integral permits the deployment of iterative quadrature schemes, thereby reducing the required number of measurements by several orders of magnitude. We further show that a modified ansatz captures deviations from the Bisognano-Wichmann form in lattice models, improves convergence, and provides a cost-function-level diagnostic for quantum phase transitions. Finally, we establish that a low cost value does not by itself guarantee convergence in trace distance. Nevertheless, it faithfully reproduces degeneracies and spectral gaps, which are essential for applications to topological phases.

Fast and Flexible Quantum-Inspired Differential Equation Solvers with Data Integration

Authors: Lucas Arenstein, Martin Mikkelsen, Michael Kastoryano

arXiv ID: 2505.17046 | Date: 2025-05-15

Abstract: Accurately solving high-dimensional partial differential equations (PDEs) remains a central challenge in computational mathematics. Traditional numerical methods, while effective in low-dimensional settings or on coarse grids, often struggle to deliver the precision required in practical applications. Recent machine learning-based approaches offer flexibility but frequently fall short in terms of accuracy and reliability, particularly in industrial contexts. In this work, we explore a quantum-inspired method based on quantized tensor trains (QTT), enabling efficient and accurate solutions to PDEs in a variety of challenging scenarios. Through several representative examples, we demonstrate that the QTT approach can achieve logarithmic scaling in both memory and computational cost for linear and nonlinear PDEs. Additionally, we introduce a novel technique for data-driven learning within the quantum-inspired framework, combining the adaptability of neural networks with enhanced accuracy and reduced training time.

Overcoming the entanglement barrier with sampled tensor networks

Authors: Stefano Carignano, Guglielmo Lami, Jacopo De Nardis, Luca Tagliacozzo

arXiv ID: 2505.09714 | Date: 2025-05-14

Abstract: The rapid growth of entanglement under unitary time evolution is the primary bottleneck for modern tensor-network techniques--such as Matrix Product States (MPS)--when computing time-dependent expectation values. This {entanglement barrier} restricts classical simulations and, conversely, underpins the quantum advantage anticipated from future devices. Here we show that, for one-dimensional Hamiltonian dynamics, the spatio-temporal tensor network encoding the evolved wave function amplitudes can be contracted efficiently along the left-right (spatial) direction. Exploiting this structure, we develop a hybrid Tensor-Network/Monte-Carlo (TN-MC) algorithm that samples the wave function and evaluates expectation values of generic local operators with computational cost that scales only polynomially in time. The accurate contraction of the wave function amplitudes is a consequence of the favorable scaling with time of the generalised temporal entropies. We find that their real part either saturates or, at most, grows logarithmically with time, revealing new instances of continuous dynamical quantum phase transitions (DQPTs) which we characterize. Our results therefore show that, when computing expectation values of local operators, the entanglement barrier in one-dimensional Hamiltonian evolution can be bypassed with a TN-MC blend.

Unified approach to the resources of tensor network and stabilizer simulations

Authors: Zhong-Xia Shang, Si-Yuan Chen, Wenjun Yu, Giulio Chiribella, Qi Zhao

arXiv ID: 2505.09512 | Date: 2025-05-14

Abstract: We introduce a general resource indicator, called the bra-ket entanglement, which can be used to bound the resource dependence of classical simulations in the tensor network framework and in the stabilizer formalism. For the tensor network framework, our bounds indicate that bra-ket entanglement governs the interplay between two physical resources, the coherence and the magic. As bra-ket entanglement increases, the dominant resource that governs the complexity of the tensor network framework, quantified by entanglement, shifts from coherence to magic. For the stabilizer formalism approach, we find that magic is always the dominant resource regardless of bra-ket entanglement. This conclusion is obtained by developing an operator stabilizer formalism, which extends the standard stabilizer formalism for pure states and has additional advantages in simulating certain quantum circuits. Therefore, our results indicate that as bra-ket entanglement increases, the resource governing the complexity of the two approaches goes from different to the same.

Vortex and fractional quantum Hall phases in a rotating anisotropic Bose gas

Authors: Umut Tanyeri, Ahmed Kallushi, Rıfat Onur Umucalılar, Ahmet Keleş

arXiv ID: 2505.09452 | Date: 2025-05-14

Abstract: Realizing fractional quantum Hall (FQH) states in ultracold atomic systems remains a major goal despite numerous experimental advances in the last few decades. Recent progress in trap anisotropy control under rapid rotation has renewed interest in ultracold atomic FQH physics, enabling experiments that impart much larger angular momentum per particle and offer in-situ imaging with resolution finer than the cyclotron orbit size. In this paper, we present a theoretical investigation of a rapidly rotating anisotropic Bose gas. By projecting the full Hamiltonian, including both kinetic and interaction terms, onto the lowest Landau level, we derive a compact two-parameter model that captures the effects of interaction strength, rotation rate, and anisotropy. Using exact diagonalization and density matrix renormalization group, we obtain a phase diagram that features broken-symmetry phases and topologically ordered quantum Hall states, while also highlighting the distinctive physics arising from the system's edges. Our results demonstrate the potential for future theoretical and experimental exploration of anisotropic quantum fluids, offering a unified framework for weakly interacting Bose condensates, vortex matter, and strongly correlated topological phases.

TensorRL-QAS: Reinforcement learning with tensor networks for improved quantum architecture search

Authors: Akash Kundu, Stefano Mangini

arXiv ID: 2505.09371 | Date: 2025-05-14

Abstract: Variational quantum algorithms hold the promise to address meaningful quantum problems already on noisy intermediate-scale quantum hardware. In spite of the promise, they face the challenge of designing quantum circuits that both solve the target problem and comply with device limitations. Quantum architecture search (QAS) automates the design process of quantum circuits, with reinforcement learning (RL) emerging as a promising approach. Yet, RL-based QAS methods encounter significant scalability issues, as computational and training costs grow rapidly with the number of qubits, circuit depth, and hardware noise. To address these challenges, we introduce TensorRL-QAS\textit{TensorRL-QAS}, an improved framework that combines tensor network methods with RL for QAS. By warm-starting the QAS with a matrix product state approximation of the target solution, TensorRL-QAS effectively narrows the search space to physically meaningful circuits and accelerates the convergence to the desired solution. Tested on several quantum chemistry problems of up to 12-qubit, TensorRL-QAS achieves up to a 10-fold reduction in CNOT count and circuit depth compared to baseline methods, while maintaining or surpassing chemical accuracy. It reduces classical optimizer function evaluation by up to 100-fold, accelerates training episodes by up to 98%\%, and can achieve 50%\% success probability for 10-qubit systems, far exceeding the <<1%\% rates of baseline. Robustness and versatility are demonstrated both in the noiseless and noisy scenarios, where we report a simulation of an 8-qubit system. Furthermore, TensorRL-QAS demonstrates effectiveness on systems on 20-qubit quantum systems, positioning it as a state-of-the-art quantum circuit discovery framework for near-term hardware and beyond.

One-dimensional extended Hubbard model coupled with an optical cavity

Authors: Taiga Nakamoto, Kazuaki Takasan, Naoto Tsuji

arXiv ID: 2505.09311 | Date: 2025-05-14

Abstract: We study the one-dimensional extended Hubbard model coupled with an optical cavity, which describes an interplay of the effect of vacuum fluctuation of light and the quantum phase transition between the charge- and spin-density-wave phases. The ground state and excitation spectrum of the model are calculated by numerically exact tensor-network methods. We find that the photon number of the ground state is enhanced (suppressed) along the quantum phase transition line when the light-matter coupling is comparable to (much smaller than) the cavity frequency. We also show that the exciton peak in the optical conductivity and photon spectrum that exists without the cavity exhibits the vacuum Rabi splitting at resonance due to the light-matter interaction. This behavior is in contrast to the case without excitons, where the photon spectrum is merely broadened without splitting due to the lack of a sharp resonance.

Quantized six-vertex model on a torus

Authors: Rei Inoue, Atsuo Kuniba, Yuji Terashima, Junya Yagi

arXiv ID: 2505.08924 | Date: 2025-05-13

Abstract: We study the integrability of the quantized six-vertex model with four parameters on a torus. It is a three-dimensional integrable lattice model in which a layer transfer matrix, depending on two spectral parameters associated with the homology cycles of the torus, can be defined not only on the square lattice but also on more general graphs. For a class of graphs that we call admissible, we establish the commutativity of the layer transfer matrices by introducing four types of tetrahedron equations and two types of inversion relations. Expanding in the spectral parameters yields a family of commuting quantum Hamiltonians. The quantized six-vertex model can also be reformulated in terms of (quantized) dimer models, and encompasses known integrable systems as special cases, including the free parafermion model and the relativistic Toda chain.

Augmenting Density Matrix Renormalization Group with Matchgates and Clifford circuits

Authors: Jiale Huang, Xiangjian Qian, Zhendong Li, Mingpu Qin

arXiv ID: 2505.08635 | Date: 2025-05-13

Abstract: Matchgates and Clifford circuits are two types of quantum circuits which can be efficiently simulated classically, though the underlying reasons are quite different. Matchgates are essentially the single particle basis transformations in the Majorana fermion representation which can be easily handled classically, while the Clifford circuits can be efficiently simulated using the tableau method according to the Gottesman-Knill theorem. In this work, we propose a new wave-function ansatz in which matrix product states are augmented with the combination of Matchgates and Clifford circuits (dubbed MCA-MPS) to take advantage of the representing power of all of them. Moreover, the optimization of MCA-MPS can be efficiently implemented within the Density Matrix Renormalization Group method. Our benchmark results on one-dimensional hydrogen chain show that MCA-MPS can improve the accuracy of the ground-state calculation by several orders of magnitude over MPS with the same bond dimension. This new method provides us a useful approach to study quantum many-body systems. The MCA-MPS ansatz also expands our understanding of classically simulatable quantum many-body states.

Distributed Quantum Neural Networks on Distributed Photonic Quantum Computing

Authors: Kuan-Cheng Chen, Chen-Yu Liu, Yu Shang, Felix Burt, Kin K. Leung

arXiv ID: 2505.08474 | Date: 2025-05-13

Abstract: We introduce a distributed quantum-classical framework that synergizes photonic quantum neural networks (QNNs) with matrix-product-state (MPS) mapping to achieve parameter-efficient training of classical neural networks. By leveraging universal linear-optical decompositions of MM-mode interferometers and photon-counting measurement statistics, our architecture generates neural parameters through a hybrid quantum-classical workflow: photonic QNNs with M(M+1)/2M(M+1)/2 trainable parameters produce high-dimensional probability distributions that are mapped to classical network weights via an MPS model with bond dimension χχ. Empirical validation on MNIST classification demonstrates that photonic QT achieves an accuracy of 95.50%±0.84%95.50\% \pm 0.84\% using 3,292 parameters (χ=10χ= 10), compared to 96.89%±0.31%96.89\% \pm 0.31\% for classical baselines with 6,690 parameters. Moreover, a ten-fold compression ratio is achieved at χ=4χ= 4, with a relative accuracy loss of less than 3%3\%. The framework outperforms classical compression techniques (weight sharing/pruning) by 6--12\% absolute accuracy while eliminating quantum hardware requirements during inference through classical deployment of compressed parameters. Simulations incorporating realistic photonic noise demonstrate the framework's robustness to near-term hardware imperfections. Ablation studies confirm quantum necessity: replacing photonic QNNs with random inputs collapses accuracy to chance level (10.0%±0.5%10.0\% \pm 0.5\%). Photonic quantum computing's room-temperature operation, inherent scalability through spatial-mode multiplexing, and HPC-integrated architecture establish a practical pathway for distributed quantum machine learning, combining the expressivity of photonic Hilbert spaces with the deployability of classical neural networks.

Bang-bang preparation of a quantum many-body ground state in a finite lattice: optimization of the algorithm with a tensor network

Authors: Ihor Sokolov, Jacek Dziarmaga

arXiv ID: 2505.08226 | Date: 2025-05-13

Abstract: A bang-bang (BB) algorithm prepares the ground state of a lattice quantum many-body Hamiltonian H=H1+H2H=H_1+H_2 by evolving an initial product state alternating between H1H_1 and H2H_2. We optimize the algorithm with tensor networks in one and two dimensions. The optimization has two stages. In stage one, a shallow translationally-invariant circuit is optimized in an infinite lattice. In stage two, the infinite-lattice gate sequence is used as a starting point for a finite lattice where it remains optimal in the bulk. The prepared state requires optimization only at its boundary, within a healing length from lattice edges, and the gate sequence needs to be modified only within the causal cone of the boundary. We test the procedure in the 1D and 2D quantum Ising model near its quantum critical point employing, respectively, the matrix product state (MPS) and the pair-entangled projected state (PEPS). At the boundary already the infinite-lattice sequence turns out to provide a more accurate state than in the bulk.

A Unifying Framework for Fractional Chern Insulator Stabilization

Authors: Peleg Emanuel, Anna Keselman, Yuval Oreg

arXiv ID: 2505.07950 | Date: 2025-05-12

Abstract: We present a theory of fractional Chern insulator stabilization against charge-ordered states. We argue that the phase competition is captured by an effective interaction range, which depends on both the bare interaction range and quantum geometric properties. We argue that short effective interaction ranges stabilize fractional states while longer-range interactions favor charge-ordered states. To confirm our hypothesis, we conduct a numerical study of the generalized Hofstadter model using the density matrix renormalization group. Our theory offers a new interpretation of the geometric stability hypothesis and generalizes it, providing a unifying framework for several approaches to fractional phase stabilization. Finally, we propose a route towards experimental verification of the theory and possible implications for fractional states in bands with higher Chern numbers.

Evidence that the Quantum Approximate Optimization Algorithm Optimizes the Sherrington-Kirkpatrick Model Efficiently in the Average Case

Authors: Sami Boulebnane, Abid Khan, Minzhao Liu, Jeffrey Larson, Dylan Herman, Ruslan Shaydulin, Marco Pistoia

arXiv ID: 2505.07929 | Date: 2025-05-12

Abstract: The Sherrington-Kirkpatrick (SK) model serves as a foundational framework for understanding disordered systems. The Quantum Approximate Optimization Algorithm (QAOA) is a quantum optimization algorithm whose performance monotonically improves with its depth pp. We analyze QAOA applied to the SK model in the infinite-size limit and provide numerical evidence that it obtains a (1ε)(1-ε) approximation to the optimal energy with circuit depth O(n/ε1.13)\mathcal{O}(n/ε^{1.13}) in the average case. Our results are enabled by mapping the task of evaluating QAOA energy onto the task of simulating a spin-boson system, which we perform with modest cost using matrix product states. We optimize QAOA parameters and observe that QAOA achieves ε2.2%\varepsilon\lesssim2.2\% at p=160p=160 in the infinite-size limit. We then use these optimized QAOA parameters to evaluate the QAOA energy for finite-sized instances with up to 3030 qubits and find convergence to the ground state consistent with the infinite-size limit prediction. Our results provide strong numerical evidence that QAOA can efficiently approximate the ground state of the SK model in the average case.

Quon Classical Simulation: Unifying Cliffords, Matchgates and Entanglement

Authors: Zixuan Feng, Zhengwei Liu, Fan Lu, Ningfeng Wang

arXiv ID: 2505.07804 | Date: 2025-05-12

Abstract: We propose a new framework of topological complexity to study the computational complexity of quantum circuits and tensor networks. Within this framework, we establish the Quon Classical Simulation (QCS) for hybrid Clifford-Matchgate circuits, which is efficient for both Clifford circuits and Matchgate circuits, therefore answering a long standing open question on unifying efficient classical simulations. This framework is built upon the Quon language, a 2+1D topological quantum field theory with space-time boundary and defects. Its exponential computation complexity is captured by Magic holes, a topological feature capturing the global long-range entanglement. Both Clifford circuits and Matchgate circuits are free of Magic holes. Efficient classical simulations of Cliffords and Matchgates are implemented by two parallel operations, generalized surgery theory of 3-manifolds and Yang-Baxter relations on the 2D boundary respectively, with additional binary arithmetic properties.

Mixed state deep thermalization

Authors: Xie-Hang Yu, Wen Wei Ho, Pavel Kos

arXiv ID: 2505.07795 | Date: 2025-05-12

Abstract: We introduce the notion of the mixed state projected ensemble (MSPE), a collection of mixed states describing a local region of a quantum many-body system, conditioned upon measurements of the complementary region which are incomplete. This constitutes a generalization of the pure state projected ensemble in which measurements are assumed ideal and complete, and which has been shown to tend towards limiting pure state distributions depending only on symmetries of the system, thus representing a new kind of universality in quantum equilibration dubbed deep thermalization. We study the MSPE generated by solvable (1+1)d dual-unitary quantum circuit evolution, and identify the limiting mixed state distributions which emerge at late times depending on the size of the incomplete measurement, which we assume to be lossy, finding that they correspond to certain random density matrix ensembles known in the literature. We also derive the rate of the emergence of such universality. Furthermore, we investigate the quantum information properties of the states composing the ensemble, specifically their capacity to teleport quantum information between the ends of the system. The teleportation fidelity is upper bounded by the quantum conditional entropy, which we find exhibits a sharp transition from zero to maximal when the number of measurements lost matches of that the number of degrees of freedom to be teleported. Our results initiate the first investigation of deep thermalization for mixed state ensembles, which are relevant for present-day quantum simulation experiments wherein measurements are typically not perfect, and also amount to a physical and natural way of sampling from hitherto abstract random density matrix ensembles.

Time evolution of the quantum Ising model in two dimensions using Tree Tensor Networks

Authors: Wladislaw Krinitsin, Niklas Tausendpfund, Markus Heyl, Matteo Rizzi, Markus Schmitt

arXiv ID: 2505.07612 | Date: 2025-05-12

Abstract: The numerical simulation of two-dimensional quantum many-body systems away from equilibrium constitutes a major challenge for all known computational methods. We investigate the utility of Tree Tensor Network (TTN) states to solve the dynamics of the quantum Ising model in two dimensions. Within the perturbative regime of small transverse fields, TTNs faithfully reproduce analytically known, but non-trivial and physically interesting results, for lattices up to 16×1616 \times 16 sites. Limitations of the method related to the rapid growth of entanglement entropy are explored within more general, paradigmatic quench settings. We provide and discuss comprehensive benchmarks regarding the benefit of \emph{GPU} acceleration and the impact of using local operator sums on the performance.

Emergence of gravity from quantum field theory in triangulated spacetime and the QFT vector model

Authors: Matti Raasakka

arXiv ID: 2505.07102 | Date: 2025-05-11

Abstract: We formulate quantum field theory in triangulated spacetime using compositional quantum field theory and tensor network methods. We show that gravitational interactions emerge as a low-energy effective phenomenon in this framework. For concrete calculations we use free massive scalar field theory in two-dimensional Lorentzian spacetime, but the results generalize to other models and higher dimensions. Finally, our results lead us to propose a new approach to the unification of quantum field theory with gravity, the QFT vector model, which combines insights and techniques from various current approaches to quantum gravity such as causal dynamical triangulations, random tensor models, group field theory, emergent gravity and holography.

Initialization and training of matrix product state probabilistic models

Authors: Xun Tang, Yuehaw Khoo, Lexing Ying

arXiv ID: 2505.06419 | Date: 2025-05-09

Abstract: Modeling probability distributions via the wave function of a quantum state is central to quantum-inspired generative modeling and quantum state tomography (QST). We investigate a common failure mode in training randomly initialized matrix product states (MPS) using gradient descent. The results show that the trained MPS models do not accurately predict the strong interactions between boundary sites in periodic spin chain models. In the case of the Born machine algorithm, we further identify a causality trap, where the trained MPS models resemble causal models that ignore the non-local correlations in the true distribution. We propose two complementary strategies to overcome the training failure -- one through optimization and one through initialization. First, we develop a natural gradient descent (NGD) method, which approximately simulates the gradient flow on tensor manifolds and significantly enhances training efficiency. Numerical experiments show that NGD avoids local minima in both Born machines and in general MPS tomography. Remarkably, we show that NGD with line search can converge to the global minimum in only a few iterations. Second, for the BM algorithm, we introduce a warm-start initialization based on the TTNS-Sketch algorithm. We show that gradient descent under a warm initialization does not encounter the causality trap and admits rapid convergence to the ground truth.

Fractional Chern Insulators and Competing States in a Twisted MoTe2_2 Lattice Model

Authors: Yuchi He, S. H. Simon, S. A. Parameswaran

arXiv ID: 2505.06354 | Date: 2025-05-09

Abstract: We construct an interacting lattice model for twisted MoTe2\mathrm{MoTe}_{2} bilayers at a twist angle of approximately 3.7\degree. We use the infinite density matrix renormalization group (iDMRG) in a cylinder geometry to identify a variety of competing integer and fractional Chern insulators and charge density wave (CDW) states that emerge upon the spontaneous breaking of time reversal symmetry by valley polarization. We use finite-size analysis to establish the robustness of Chern insulating states even in geometries that admit competing CDWs, and explore the phase transitions between these states driven by increasing sublattice potential or interaction strength. Our work highlights the crucial role played by direct spin exchange in stabilizing the parent valley-polarized Chern ferromagnet band, and by the mixing with higher bands in destabilizing CIs/FCIs in favor of CDW orders.

Emergent magnetism and spin liquids in an extended Hubbard description of moiré bilayers

Authors: Zhenhao Song, Urban F. P. Seifert, Leon Balents, Hong-Chen Jiang

arXiv ID: 2505.06339 | Date: 2025-05-09

Abstract: Motivated by twisted transition metal dichalcogenides (TMDs), we study an extended Hubbard model with both on-site and off-site repulsive interactions, in which Mott insulating states with concomitant charge order occur at fractional fillings. To resolve the charge ordering as well as the fate of the local moments formed thereby, we perform large-scale density matrix renormalization group calculations on cylindrical geometries for several filling fractions and ranges of interaction strength. Depending on the precise parameter regime, both antiferromagnetically ordered as well as quantum-disordered states are found, with a particularly prominent example being a quantum spin liquid-type ground state on top of charge-ordering with effective Kagomé geometry. We discuss the different mechanisms at play in stabilizing various electronic and magnetic states. The results suggest that moiré TMDs are a promising venue for emergent quantum magnetism of strongly interacting electrons.

2D Quon Language: Unifying Framework for Cliffords, Matchgates, and Beyond

Authors: Byungmin Kang, Chen Zhao, Zhengwei Liu, Xun Gao, Soonwon Choi

arXiv ID: 2505.06336 | Date: 2025-05-09

Abstract: Simulating generic quantum states and dynamics is practically intractable using classical computers. However, certain special classes -- namely Clifford and matchgate circuits -- permit efficient computation. They provide invaluable tools for studying many-body physics, quantum chemistry, and quantum computation. While both play foundational roles across multiple disciplines, the origins of their tractability seem disparate, and their relationship remain unclear. A deeper understanding of such tractable classes could expand their scope and enable a wide range of new applications. In this work, we make progress toward the unified understanding of the Clifford and matchgate -- these two classes are, in fact, distinct special cases of a single underlying structure. Specifically, we introduce the 2D Quon language, which combines Majorana worldlines with their underlying spacetime topology to diagrammatically represent quantum processes and tensor networks. In full generality, the 2D Quon language is universal -- capable of representing arbitrary quantum states, dynamics, or tensor networks -- yet they become especially powerful in describing Clifford and matchgate classes. Each class can be efficiently characterized in a visually recognizable manner using the Quon framework. This capability naturally gives rise to several families of efficiently computable tensor networks introduced in this work: punctured matchgates, hybrid Clifford-matchgate-MPS, and ansatze generated from factories of tractable networks. All of these exhibit high non-Cliffordness, high non-matchgateness, and large bipartite entanglement entropy. We discuss a range of applications of our approach, from recovering well-known results such as the Kramers-Wannier duality and the star-triangle relation of the Ising model, to enabling variational optimization with novel ansatz states.

Distributed Tensor Network Library for Quantum Computing Emulation

Authors: Jakub Adamski, Oliver Thomson Brown

arXiv ID: 2505.06119 | Date: 2025-05-09

Abstract: Tensor networks offer an adaptable and efficient approach to emulation of quantum computers. Their usage relies on partitioning circuits into small tensors, which are contracted together to form the final result. While this approach intends to minimise the problem size, exceeding the locally available memory is sometimes unavoidable due to the exponential nature of quantum systems. Most HPC tensor network packages tackle this issue with a procedure called circuit slicing, which distributes the entire network onto multiple ranks, recombining it back when necessary. In this study, we present a novel alternative approach, where individual tensors are both broadcast and scattered to harness multiple levels of parallelism. The technique is abstracted behind a fixed distribution pattern, and actualised in a new portable tensor network library, QTNH, built on top of MPI and ScaLAPACK. We showcase its capabilities on ARCHER2, by emulating two well-known algorithms - the Quantum Fourier Transform and Random Circuit Sampling. This is accomplished by leveraging the implemented operations to realise various contraction strategies, including a unique distributed MPS tensor factorisation approach. We thus demonstrate that our library can be used to advance the accuracy of quantum emulation, while offering a simple and flexible interface to tensor distribution.

TTNOpt: Tree tensor network package for high-rank tensor compression

Authors: Ryo Watanabe, Hidetaka Manabe, Toshiya Hikihara, Hiroshi Ueda

arXiv ID: 2505.05908 | Date: 2025-05-09

Abstract: We have developed TTNOpt, a software package that utilizes tree tensor networks (TTNs) for quantum spin systems and high-dimensional data analysis. TTNOpt provides efficient and powerful TTN computations by locally optimizing the network structure, guided by the entanglement pattern of the target tensors. For quantum spin systems, TTNOpt searches for the ground state of Hamiltonians with bilinear spin interactions and magnetic fields, and computes physical properties of these states, including the variational energy, bipartite entanglement entropy (EE), single-site expectation values, and two-site correlation functions. Additionally, TTNOpt can target the lowest-energy state within a specified subspace, provided that the Hamiltonian conserves total magnetization. For high-dimensional data analysis, TTNOpt factorizes complex tensors into TTN states that maximize fidelity to the original tensors by optimizing the tensors and the network. When a TTN is provided as input, TTNOpt reconstructs the network based on the EE without referencing the fidelity of the original state. We present three demonstrations of TTNOpt: (1) Ground-state search for the hierarchical chain model with a system size of 256256. The entanglement patterns of the ground state manifest themselves in a tree structure, and TTNOpt successfully identifies the tree. (2) Factorization of a quantic tensor of the 2242^{24} dimensions representing a three-variable function where each variant has a weak bit-wise correlation. The optimized TTN shows that its structure isolates the variables from each other. (3) Reconstruction of the matrix product network representing a 1616-variable normal distribution characterized by a tree-like correlation structure. TTNOpt can reveal hidden correlation structures of the covariance matrix.

Topological Devil's staircase in a constrained kagome Ising antiferromagnet

Authors: Afonso Rufino, Samuel Nyckees, Jeanne Colbois, Frédéric Mila

arXiv ID: 2505.05889 | Date: 2025-05-09

Abstract: We show that the constrained Ising model on the kagome lattice with infinite first and third neighbor couplings undergoes an infinite series of thermal first-order transitions at which, as in the Kasteleyn transition, linear defects of infinite length condense. However, their density undergoes abrupt jumps because of the peculiar structure of the low temperature phase, which is only partially ordered and hosts a finite density of zero-energy domain walls. The number of linear defects between consecutive zero-energy domain walls is quantized to integer values, leading to a devil's staircase of topological origin. By contrast to the devil's staircase of the ANNNI and related models, the wave-vector is not fixed to commensurate values inside each phase.

Towards secondary structure prediction of longer mRNA sequences using a quantum-centric optimization scheme

Authors: Vaibhaw Kumar, Dimitris Alevras, Mihir Metkar, Eline Welling, Chris Cade, Ido Niesen, Triet Friedhoff, Jae-Eun Park, Saurabh Shivpuje, Mariana LaDue, Wade Davis, Alexey Galda

arXiv ID: 2505.05782 | Date: 2025-05-09

Abstract: Accurate prediction of mRNA secondary structure is critical for understanding gene expression, translation efficiency, and advancing mRNA-based therapeutics. However, the combinatorial complexity of possible foldings, especially in long sequences, poses significant computational challenges for classical algorithms. In this work, we propose a scalable, quantum-centric optimization framework that integrates quantum sampling with classical post-processing to tackle this problem. Building on a Quadratic Unconstrained Binary Optimization (QUBO) formulation of the mRNA folding task, we develop two complementary workflows: a Conditional Value at Risk (CVaR)-based variational quantum algorithm enhanced with gauge transformations and local search, and an Instantaneous Quantum Polynomial (IQP) circuit-based scheme where training is done classically and sampling is delegated to quantum hardware. We demonstrate the effectiveness of these approaches using IBM quantum processors, solving problem instances with up to 156 qubits and circuits containing up to 950 nonlocal gates, corresponding to mRNA sequences of up to 60 nucleotides. Additionally, we validate scalability of the CVaR algorithm on a tensor network simulator, reaching up to 354 qubits in noiseless settings. These results demonstrate the growing practical capabilities of hybrid quantum-classical methods for tackling large-scale biological optimization problems.

Lévy Light Cones and Critical Causality in Fractional Multiscale Quantum Ising Models

Authors: Joshua M Lewis, Zhexuan Gong, Lincoln D Carr

arXiv ID: 2505.05645 | Date: 2025-05-08

Abstract: We study causality and criticality in a one-dimensional fractional multiscale transverse-field Ising model, where fractional derivatives generate long range interactions beyond the scope of standard power laws. Such fractional responses are common in classical systems including the anomalous stress-strain behaviour of viscoelastic polymers, Lévy-like contaminant transport in heterogeneous porous media, and the non-Debye dielectric relaxation of glassy dielectrics. Furthermore, these unique interactions can be implemented in current quantum information architectures, with intriguing consequences for the many-body dynamics. Using a truncated Jordan-Wigner approach, we show that in the long wavelength limit of the mean field, the dynamical critical exponent is set by the fractional order q as z=q/2z=q/2. To probe genuine many-body dynamics, we apply matrix-product-state simulations with the time-dependent variational principle adapted to nonlocal couplings. Tracking the entanglement-entropy light cone and performing finite-size scaling of the many-body gap for 0<q<2.50<q<2.5, we confirm a continuously tunable exponent z(q)z(q): for q<2q<2 the entanglement front broadens with a sublinear light cone; for 2<q<2.52<q<2.5 we observe a faint superlinear cone indicative of z<1z<1; and for q2.5q \gtrsim 2.5 the system reverts to the ballistic nearest-neighbour regime with z=1z=1. The correspondence between quantum entanglement fronts that spread as t1/zt^{1/z} and classical Lévy flights whose mean-square displacement grows as t2/qt^{2/q} provides a direct physical link between fractional interactions and Lévy statistics. Fractional derivatives therefore offer a unified framework in which short-range, power-law, and frustrated long-range interactions emerge as limiting cases, enabling controlled exploration of nonlocal causality bounds and exotic entanglement dynamics within current quantum information platforms.

Asymmetric decay of quantum many-body scars in XYZ quantum spin chains

Authors: Dhiman Bhowmick, Vir B. Bulchandani, Wen Wei Ho

arXiv ID: 2505.05435 | Date: 2025-05-08

Abstract: Quantum many-body scars are atypical energy eigenstates of chaotic quantum many-body systems that prevent certain special non-equilibrium initial conditions from thermalizing. We point out that quantum many-body scars exist for any nearest-neighbor spin-SS XYZ quantum spin chain, and arise in the form of an infinite family of highly excited yet nonentangled product-state eigenstates, which define periodic textures in spin space. This set of scars, discovered originally by Granovskii and Zhedanov in 1985, encompasses both the experimentally relevant 'spin helices' for XXZ chains and more complicated helix-like states constructed from Jacobi elliptic functions for generic XYZ chains. An appealing feature of Granovskii-Zhedanov scars is that they are well-defined in the semiclassical limit SS \to \infty, which allows for a systematic and analytical treatment of their dynamical instability to perturbations of the Hamiltonian. Using time-dependent spin-wave theory, we predict that upon perturbing along certain directions in Hamiltonian space, Granovskii-Zhedanov scars exhibit a dramatic asymmetry in their decay: depending on the sign of the perturbation, the decrease of their contrast is either slow and linear, or fast and exponential in time. This asymmetry can be traced to the absence (presence) of imaginarity in the spectrum of the Bogoliubov Hamiltonian governing quantum fluctuations about the scar, which corresponds to the absence (presence) of a non-zero Lyapunov exponent for the limiting classical trajectory. Numerical simulations using matrix product states (MPS) and infinite time-evolving block decimation (iTEBD) confirm that our prediction remains valid even far from the semiclassical limit. Our findings challenge existing theories of how quantum-many body scars relax.

Quantum selection of order and dynamic properties of Kitaev-Heisenberg ferromagnet on a triangular lattice

Authors: Kaushal K. Kesharpu, Pavel A. Maksimov

arXiv ID: 2505.05204 | Date: 2025-05-08

Abstract: Recent interest in monolayer materials motivated a search for two-dimensional ferromagnets with sizable spin-orbit coupling. Magnetic anisotropy of exchange Hamiltonian, induced by spin-orbit coupling, may not only stabilize long-range order, but also in turn can be a source of frustration and accidental degeneracy, which is the case for the Kitaev-Heisenberg model. Here we present an extensive study of ground state and excitations of ferromagnetic anisotropic-exchange Kitaev-Heisenberg model on a triangular lattice using order-by-disorder and augmented spin-wave theory calculations. It is shown that while bond-dependent terms of the model do not affect the ground state classically, quantum fluctuations select preferred magnetization direction of the ferromagnetic state and significantly alter classical phase diagram. Anisotropic terms of the magnetic Hamiltonian also give rise to magnon-magnon interactions that lead to spontaneous decay and spectral renormalization, which we illustrate using non-linear spin-wave theory.

Two-dimensional J1J_1-J2J_2 clock model: Enhanced symmetries, emergent orders, and Landau-incompatible transitions

Authors: Vishnu Pulloor Kuttanikkad, Abhishodh Prakash, Rajesh Narayanan, Titas Chanda

arXiv ID: 2505.05194 | Date: 2025-05-08

Abstract: We present a comprehensive study on the frustrated J1J_1-J2J_2 classical qq-state clock model with even q>4q>4 on a two-dimensional square lattice, revealing a rich ensemble of phases driven by competing interactions. In the unfrustrated regime (J1>2J2J_1>2J_2), the model reproduces the standard clock model phenomenology: a low-temperature Zq\mathbb{Z}_q-broken ferromagnet, an intermediate XY-like critical quasi-long-range-ordered (QLRO) phase with emergent U(1)U(1) symmetry, and a high-temperature paramagnet. For J1<2J2J_1<2J_2, frustration stabilizes five distinct regimes: the disordered paramagnet, a stripe-ordered phase breaking Zq×Z2\mathbb{Z}_q\times\mathbb{Z}_2 symmetry, two Z2\mathbb{Z}_2-broken nematic phases (one with and one without QLRO), and an exotic stripe phase with emergent discrete Zq\mathbb{Z}_q spin degrees of freedom prohibited in the microscopic Hamiltonian. Remarkably, this seemingly forbidden Zq\mathbb{Z}_q order emerges via a relevant operator in the infrared long-wavelength limit, rather than from an irrelevant perturbation, highlighting a non-standard route to emergence. Using large-scale corner transfer matrix renormalization group calculations, complemented by classical Monte Carlo simulations, we map the complete phase diagram and identify Berezinskii-Kosterlitz-Thouless, Ising, first-order, and unconventional Landau-incompatible transitions between different phases. Finally, we propose an effective field-theoretic framework that encompasses these emergent orders and their interwoven transitions.

Planar fault-tolerant circuits for non-Clifford gates on the 2D color code

Authors: Andreas Bauer, Julio C. Magdalena de la Fuente

arXiv ID: 2505.05175 | Date: 2025-05-08

Abstract: We introduce a family of scalable planar fault-tolerant circuits that implement logical non-Clifford operations on a 2D color code, such as a logical TT gate or a logical non-Pauli measurement that prepares a magic T|T\rangle state. The circuits are relatively simple, consisting only of physical TT gates, CXCX gates, and few-qubit measurements. They can be implemented with an array of qubits on a 2D chip with nearest-neighbor couplings, and no wire crossings. The construction is based on a spacetime path integral representation of a non-Abelian 2+1D topological phase, which is related to the 3D color code. We turn the path integral into a circuit by expressing it as a spacetime ZXZX tensor network, and then traversing it in some chosen time direction. We describe in detail how fault tolerance is achieved using a "just-in-time" decoding strategy, for which we repurpose and extend state-of-the-art color-code matching decoders.

Boosting Binomial Exotic Option Pricing with Tensor Networks

Authors: Maarten van Damme, Rishi Sreedhar, Martin Ganahl

arXiv ID: 2505.17033 | Date: 2025-05-07

Abstract: Pricing of exotic financial derivatives, such as Asian and multi-asset American basket options, poses significant challenges for standard numerical methods such as binomial trees or Monte Carlo methods. While the former often scales exponentially with the parameters of interest, the latter often requires expensive simulations to obtain sufficient statistical convergence. This work combines the binomial pricing method for options with tensor network techniques, specifically Matrix Product States (MPS), to overcome these challenges. Our proposed methods scale linearly with the parameters of interest and significantly reduce the computational complexity of pricing exotics compared to conventional methods. For Asian options, we present two methods: a tensor train cross approximation-based method for pricing, and a variational pricing method using MPS, which provides a stringent lower bound on option prices. For multi-asset American basket options, we combine the decoupled trees technique with the tensor train cross approximation to efficiently handle baskets of up to m=8m = 8 correlated assets. All approaches scale linearly in the number of discretization steps NN for Asian options, and the number of assets mm for multi-asset options. Our numerical experiments underscore the high potential of tensor network methods as highly efficient simulation and optimization tools for financial engineering.

Explaining Anomalies with Tensor Networks

Authors: Hans Hohenfeld, Marius Beuerle, Elie Mounzer

arXiv ID: 2505.03911 | Date: 2025-05-06

Abstract: Tensor networks, a class of variational quantum many-body wave functions have attracted considerable research interest across many disciplines, including classical machine learning. Recently, Aizpurua et al. demonstrated explainable anomaly detection with matrix product states on a discrete-valued cyber-security task, using quantum-inspired methods to gain insight into the learned model and detected anomalies. Here, we extend this framework to real-valued data domains. We furthermore introduce tree tensor networks for the task of explainable anomaly detection. We demonstrate these methods with three benchmark problems, show adequate predictive performance compared to several baseline models and both tensor network architectures' ability to explain anomalous samples. We thereby extend the application of tensor networks to a broader class of potential problems and open a pathway for future extensions to more complex tensor network architectures.

Typical Machine Learning Datasets as Low-Depth Quantum Circuits

Authors: Florian J. Kiwit, Bernhard Jobst, Andre Luckow, Frank Pollmann, Carlos A. Riofrío

arXiv ID: 2505.03399 | Date: 2025-05-06

Abstract: Quantum machine learning (QML) is an emerging field that investigates the capabilities of quantum computers for learning tasks. While QML models can theoretically offer advantages such as exponential speed-ups, challenges in data loading and the ability to scale to relevant problem sizes have prevented demonstrations of such advantages on practical problems. In particular, the encoding of arbitrary classical data into quantum states usually comes at a high computational cost, either in terms of qubits or gate count. However, real-world data typically exhibits some inherent structure (such as image data) which can be leveraged to load them with a much smaller cost on a quantum computer. This work further develops an efficient algorithm for finding low-depth quantum circuits to load classical image data as quantum states. To evaluate its effectiveness, we conduct systematic studies on the MNIST, Fashion-MNIST, CIFAR-10, and Imagenette datasets. The corresponding circuits for loading the full large-scale datasets are available publicly as PennyLane datasets and can be used by the community for their own benchmarks. We further analyze the performance of various quantum classifiers, such as quantum kernel methods, parameterized quantum circuits, and tensor-network classifiers, and we compare them to convolutional neural networks. In particular, we focus on the performance of the quantum classifiers as we introduce nonlinear functions of the input state, e.g., by letting the circuit parameters depend on the input state.

HMAE: Self-Supervised Few-Shot Learning for Quantum Spin Systems

Authors: Ibne Farabi Shihab, Sanjeda Akter, Anuj Sharma

arXiv ID: 2505.03140 | Date: 2025-05-06

Abstract: Quantum machine learning for spin and molecular systems faces critical challenges of scarce labeled data and computationally expensive simulations. To address these limitations, we introduce Hamiltonian-Masked Autoencoding (HMAE), a novel self-supervised framework that pre-trains transformers on unlabeled quantum Hamiltonians, enabling efficient few-shot transfer learning. Unlike random masking approaches, HMAE employs a physics-informed strategy based on quantum information theory to selectively mask Hamiltonian terms based on their physical significance. Experiments on 12,500 quantum Hamiltonians (60% real-world, 40% synthetic) demonstrate that HMAE achieves 85.3% ±\pm 1.5% accuracy in phase classification and 0.15 ±\pm 0.02 eV MAE in ground state energy prediction with merely 10 labeled examples - a statistically significant improvement (p < 0.01) over classical graph neural networks (78.1% ±\pm 2.1%) and quantum neural networks (76.8% ±\pm 2.3%). Our method's primary advantage is exceptional sample efficiency - reducing required labeled examples by 3-5x compared to baseline methods - though we emphasize that ground truth values for fine-tuning and evaluation still require exact diagonalization or tensor networks. We explicitly acknowledge that our current approach is limited to small quantum systems (specifically limited to 12 qubits during training, with limited extension to 16-20 qubits in testing) and that, while promising within this regime, this size restriction prevents immediate application to larger systems of practical interest in materials science and quantum chemistry.

Sequential Generation of Two-dimensional Super-area-law States with Local Parent Hamiltonian

Authors: Wucheng Zhang

arXiv ID: 2505.02914 | Date: 2025-05-05

Abstract: We construct examples of highly entangled two-dimensional states by exploiting a correspondence between stochastic processes in dd dimensions and quantum states in d+1d+1 dimensions. The entanglement structure of these states, which we explicitly calculate, can be tuned between area law, sub-volume law, and volume law. This correspondence also enables a sequential generation protocol: the states can be prepared through a series of unitary transformations acting on an auxiliary system. We also discuss the conditions under which these states have local, frustration-free parent Hamiltonians.

Partons from stabilizer codes

Authors: Rafael A. Macedo, Carlo C. Bellinati, Weslei B. Fontana, Eric C. Andrade, Rodrigo G. Pereira

arXiv ID: 2505.02683 | Date: 2025-05-05

Abstract: The Gutzwiller projection of fermionic wave functions is a well-established method for generating variational wave functions describing exotic states of matter, such as quantum spin liquids. We investigate the conditions under which a projected wave function constructed from fermionic partons can be rigorously shown to possess topological order. We demonstrate that these conditions can be precisely determined in the case of projected Majorana stabilizer codes. We then use matrix product states to study states that interpolate between two distinct Majorana fermion codes, one yielding a Z2\mathbb Z_2 spin liquid and the other a trivial polarized state upon projection. While the free-fermion states are adiabatically connected, we find that the projected states undergo a phase transition detected by the topological entanglement entropy. Our work underscores the profound impact of the Gutzwiller projection and cautions against inferring properties of quantum spin liquids solely from their unprojected counterparts.

Quantum Information Geometry Meets DMRG: Uhlmann Gauge Improvements in Computational Methods

Authors: Andrei Tudor Patrascu

arXiv ID: 2505.11514 | Date: 2025-05-05

Abstract: We introduce and systematically investigate a novel approach combining the Uhlmann gauge bundle with Density Matrix Renormalization Group (DMRG) and Matrix Product State (MPS) techniques to enhance the representation and preservation of quantum coherence in strongly correlated many-body systems. Conventional DMRG and MPS methods frequently encounter limitations when dealing with subtle quantum correlations and entanglement structures near critical points, avoided crossings, and topologically ordered phases. By integrating the dynamical Uhlmann gauge potential and its categorical extensions into the numerical optimization and truncation procedures, our approach substantially improves coherence stability and accuracy. Through illustrative applications in quantum chemistry, condensed matter physics, and quantum dynamics, we demonstrate significant enhancements in precision and reliability, underscoring the broad potential of Uhlmann gauge-enhanced computational methods.

Exact diagonalization study of triangular Heisenberg model with four-spin ring-exchange interaction

Authors: Yuchao Zheng, Muwei Wu, Dao-Xin Yao, Han-Qing Wu

arXiv ID: 2505.02030 | Date: 2025-05-04

Abstract: Using Lanczos exact diagonalization (ED), we study the spin-1/2 J1J_1-J2J_2 Heisenberg model with the four-spin ring-exchange interaction JrJ_r on triangular lattice. We mainly use the level spectroscopic technique of two 36-site tori to investigate the ground-state phase diagram, and further characterize phases by spin, dimer and chiral correlation functions. The ground state has rich phases including several magnetic ordered phases like zigzag phase and tetrahedral phase, as well as several novel nonmagnetic phases, some of which exhibit valence bond solid behavior in their dimer correlation functions. However, we do not find direct evidence of a quantum spin liquid phase with spinon Fermi surface in this model. Our results can give a better understanding of the ground-state properties of the triangular Heisenberg model with ring-exchange interaction, and help to understand the relevant triangular materials.

A Matrix Product State Representation of Boolean Functions

Authors: Umut Eren Usturali, Claudio Chamon, Andrei E. Ruckenstein, Eduardo R. Mucciolo

arXiv ID: 2505.01930 | Date: 2025-05-03

Abstract: We introduce a novel normal form representation of Boolean functions in terms of products of binary matrices, hereafter referred to as the Binary Matrix Product (BMP) representation. BMPs are analogous to the Tensor-Trains (TT) and Matrix Product States (MPS) used, respectively, in applied mathematics and in quantum many-body physics to accelerate computations that are usually inaccessible by more traditional approaches. BMPs turn out to be closely related to Binary Decision Diagrams (BDDs), a powerful compressed representation of Boolean functions invented in the late 80s by Bryant that has found a broad range of applications in many areas of computer science and engineering. We present a direct and natural translation of BMPs into Binary Decision Diagrams (BDDs), and derive an elementary set of operations used to manipulate and combine BMPs that are analogous to those introduced by Bryant for BDDs. Both BDDs and BMPs are practical tools when the complexity of these representations, as measured by the maximum bond dimension of a BMP (or the accumulated bond dimension across the BMP matrix train) and the number of nodes of a BDD, remains polynomial in the number of bits, nn. In both cases, controlling the complexity hinges on optimizing the order of the Boolean variables. BMPs offer the advantage that their construction and manipulation rely on simple linear algebra -- a compelling feature that can facilitate the development of open-source libraries that are both more flexible and easier to use than those currently available for BDDs. An initial implementation of a BMP library is available on GitHub, with the expectation that the close conceptual connection to TT and MPS techniques will motivate further development of BMP methods by researchers in these fields, potentially enabling novel applications to classical and quantum computing.

FTNILO: Explicit Multivariate Function Inversion, Optimization and Counting, Cryptography Weakness and Riemann Hypothesis Solution Equation with Tensor Networks

Authors: Alejandro Mata Ali

arXiv ID: 2505.05493 | Date: 2025-05-03

Abstract: In this paper, we present a new formalism, the Field Tensor Network Integral Logical Operator (FTNILO), to obtain the explicit equation that returns the minimum, maximum, and zeros of a multivariable injective function, and an algorithm for non-injective ones. This method extends the MeLoCoToN algorithm for inversion and optimization problems with continuous variables, by using Field Tensor Networks. The fundamentals of the method are the conversion of the problem of minimization of NN continuous variables into a problem of maximization of a dependent functional of a single variable. It can also be adapted to determine other properties, such as the zeros of any function. For this purpose, we use an extension of the imaginary time evolution, the new method of continuous signals, and partial or total integration, depending on the case. In addition, we show a direct way to recover both the tensor networks and the MeLoCoToN from this formalism. We show some examples of application, such as the Riemann hypothesis resolution. We provide an explicit integral equation that gives the solution of the Riemann hypothesis, being that if it results in a zero value, it is correct; otherwise, it is wrong. This algorithm requires no deep mathematical knowledge and is based on simple mathematical properties.

Polarization-Driven Charge Frustration and Emergent Phases in the One-Dimensional Extended Hubbard Model

Authors: Sourabh Saha, Jeroen van den Brink, Manoranjan Kumar, Satoshi Nishimoto

arXiv ID: 2505.01725 | Date: 2025-05-03

Abstract: Frustration is a key driver of exotic quantum phases, yet its role in charge dynamics remains largely unexplored. We show that charge frustration - induced by electronic polarization effects - stabilizes unconventional insulating states in the one-dimensional extended Hubbard model. Using exact diagonalization and density-matrix renormalization group, we uncover a charge-disordered phase that remains insulating despite lacking long-range order and possessing an effectively attractive on-site interaction - a behavior reminiscent of gapful spin liquids in frustrated spin systems. We also identify a fragile ferroelectric phase and a charge-density-wave state with emergent eight-site periodicity. These findings establish charge frustration, driven by charge-dipole interactions, as a robust mechanism for realizing exotic phases in low-dimensional correlated systems, with implications for organic conductors, transition-metal oxides, and ultracold polar molecules.

Fractionalized fermionic multicriticality in anisotropic Kitaev spin-orbital liquids

Authors: Max Fornoville, Lukas Janssen

arXiv ID: 2505.01493 | Date: 2025-05-02

Abstract: We study the low-temperature phase diagram of quantum Kitaev-Heisenberg spin-orbital models with XXZ anisotropy on the honeycomb lattice. Within a parton mean-field theory, we identify three different quantum phases, distinguished by their symmetries. Besides a disordered spin-orbital liquid with unbroken U(1) x Z2 spin rotational symmetry, there are two orbital liquid phases characterized by spin long-range order. In these phases, the spin rotational symmetry is spontaneously broken down to residual U(1) and Z2 symmetries, respectively. The symmetric spin-orbital liquid features three flavors of linearly dispersing gapless Majorana fermions. In the symmetry-broken phases, one of the three Majorana excitations remains gapless, while the other two acquire a band gap. The transitions from the symmetric to the symmetry-broken phases are continuous and fall into the fractionalized Gross-Neveu-Z2* and Gross-Neveu-SO(2)* universality classes, respectively. The transition between the ordered phases is discontinuous. Using a renormalization group analysis based on the epsilon expansion, we demonstrate that the triple point in the phase diagram features fractionalized fermionic multicriticality with emergent SO(3) symmetry.

QCMaquis 4.0: Multi-Purpose Electronic, Vibrational, and Vibronic Structure and Dynamics Calculations with the Density Matrix Renormalization Group

Authors: Kalman Szenes, Nina Glaser, Mihael Erakovic, Valentin Barandun, Maximilian Mörchen, Robin Feldmann, Stefano Battaglia, Alberto Baiardi, Markus Reiher

arXiv ID: 2505.01405 | Date: 2025-05-02

Abstract: QCMaquis is a quantum chemistry software package for general molecular structure calculations in a matrix product state/matrix product operator formalism of the density matrix renormalization group (DMRG). It supports a wide range of features for electronic structure, multi-component (pre-Born-Oppenheimer), anharmonic vibrational structure, and vibronic calculations. In addition to the ground and excited state solvers, QCMaquis allows for time propagation of matrix product states based on the tangent-space formulation of time-dependent DMRG. The latest developments include transcorrelated electronic structure calculations, very recent vibrational and vibronic models, and a convenient Python wrapper, facilitating the interface with external libraries. This paper reviews all the new features of QCMaquis and demonstrates them with new results.

Topological pump and its plateau transitions of NN-leg spin ladder

Authors: Kota Yamamoto, Yoshihito Kuno, Tomonari Mizoguchi, Kazuki Sone, Yasuhiro Hatsugai

arXiv ID: 2505.01153 | Date: 2025-05-02

Abstract: A topological pump on an N-N\textrm{-}leg spin ladder is discussed by introducing spatial clusterization whose adiabatic limit is a set of 2N-2N\textrm{-}site staircase clusters. We set a pump path in the parameter space that connects two different symmetry protected topological phases. By introducing a symmetry breaking staggered magnetic field, the system is always gapped during the pump. In the topological pump {thus obtained}, the bulk Chern number is given by the number of the critical points enclosed by the pump path. Plateau transitions characterized by the Chern number are demonstrated associated with deformation of the pump path. We find that there are NN critical points enclosed by the pump path for the N-N\textrm{-}leg ladder. The ground state phase diagram without symmetry breaking terms is numerically investigated by using the quantized Berry phase. We also discuss the physical picture of edge states in the diagonal boundary, and numerically demonstrate the bulk-edge correspondence for N=2,3N=2,3 cases.

Quasi-local Frustration-Free Free Fermions

Authors: Shunsuke Sengoku, Hoi Chun Po, Haruki Watanabe

arXiv ID: 2505.01010 | Date: 2025-05-02

Abstract: Recent studies have revealed that frustration-free models, expressed as sums of finite-range interactions or hoppings, exhibit several properties markedly different from those of frustrated models. In this work, we demonstrate that, by relaxing the finite-range condition to allow for exponentially decaying hoppings, one can build gapped frustration-free systems that realize Chern insulators as well as quasi-degenerate ground states with finite-size splittings. Moreover, by permitting power-law decaying hoppings, we also construct a gapless band metal whose finite-size gap scales inversely with the system size LL. These findings serve as an important step toward clarifying the general properties of frustration-free systems and those represented by tensor network states.

Symmetry-adapted sample-based quantum diagonalization: Application to lattice model

Authors: Kosuke Nogaki, Steffen Backes, Tomonori Shirakawa, Seiji Yunoki, Ryotaro Arita

arXiv ID: 2505.00914 | Date: 2025-05-01

Abstract: We present a symmetry-adapted extension of sample-based quantum diagonalization (SQD) that rigorously embeds space-group symmetry into the many-body subspace sampled by quantum hardware. The method is benchmarked on the two-leg ladder Hubbard model using both molecular orbital and momentum bases. Energy convergence is shown to be improved in the momentum basis compared to the molecular orbital basis for both the spin-quintet ground state and the spin-singlet excited state. We clarify the relationship between the compactness of the many-body wave function and the sparsity of the representation matrices of symmetry operations. Furthermore, the enhancement of the superconducting correlation function due to the Coulomb interaction is demonstrated. Our method highlights the importance of symmetry structure in random-sampling quantum simulation of correlated systems

Quantum Computing in Industrial Environments: Where Do We Stand and Where Are We Headed?

Authors: Eneko Osaba, Iñigo Perez Delgado, Alejandro Mata Ali, Pablo Miranda-Rodriguez, Aitor Moreno Fdez de Leceta, Luka Carmona Rivas

arXiv ID: 2505.00891 | Date: 2025-05-01

Abstract: This article explores the current state and future prospects of quantum computing in industrial environments. Firstly, it describes three main paradigms in this field of knowledge: gate-based quantum computers, quantum annealers, and tensor networks. The article also examines specific industrial applications, such as bin packing, job shop scheduling, and route planning for robots and vehicles. These applications demonstrate the potential of quantum computing to solve complex problems in the industry. The article concludes by presenting a vision of the directions the field will take in the coming years, also discussing the current limitations of quantum technology. Despite these limitations, quantum computing is emerging as a powerful tool to address industrial challenges in the future.

Simple Holography in General Spacetimes

Authors: Raphael Bousso, Elisa Tabor

arXiv ID: 2505.00695 | Date: 2025-05-01

Abstract: The simple or "outermost" wedge in AdS is the portion of the entanglement wedge that can be reconstructed with sub-exponential effort from CFT data. Here we furnish a definition in arbitrary spacetimes: given an input wedge aa analogous to a CFT boundary region, the simple wedge z(a)z(a) is the largest wedge accessible by a "zigzag," a certain sequence of antinormal lightsheets. We show that z(a)z(a) is a throat, and that it is contained in every other throat. This implies that z(a)z(a) is unique; that it is contained in the generalized entanglement wedge; and that it reduces to the AdS prescription as a special case. The zigzag explicitly constructs a preferred Cauchy slice that renders the simple wedge accessible from aa; thus it adds a novel structure even in AdS. So far, no spacelike construction is known to reproduce these results, even in time-symmetric settings. This may have implications for the modeling of holographic encoding by tensor networks.

Strange correlator and string order parameter for non-invertible symmetry protected topological phases in 1+1d

Authors: Da-Chuan Lu, Fu Xu, Yi-Zhuang You

arXiv ID: 2505.00673 | Date: 2025-05-01

Abstract: In this paper, we construct strange correlators and string order parameters for non-invertible symmetry protected topological phases (NISPTs) in 1+1d quantum lattice spin models. The strange correlator exhibits long-range order when evaluated between two distinct NISPTs and decays exponentially otherwise. We show that strange charged operators inserted into the strange correlator are linked to the interface algebra (boundary tube algebra) and are non-trivial when all its irreducible representations have dimensions greater than one. We discuss the generalization to higher dimensions. The string order parameter is obtained by contracting the truncated symmetry operator with charge decoration operators, which are determined by the NISPT action tensors. We illustrate the above construction using the three NISPTs of Rep(D8)\text{Rep}(D_8) and demonstrate the extraction of categorical data via tensor networks, particularly through the ZX calculus. Finally, we show that the entanglement spectrum degeneracy is determined by the irreducible representations of the interface algebra when assuming non-invertible symmetry on-site condition.

Accelerating two-dimensional tensor network contractions using QR-decompositions

Authors: Yining Zhang, Qi Yang, Philippe Corboz

arXiv ID: 2505.00494 | Date: 2025-05-01

Abstract: Infinite projected entangled-pair states (iPEPS) provide a powerful tool for studying strongly correlated systems directly in the thermodynamic limit. A core component of the algorithm is the approximate contraction of the iPEPS, where the computational bottleneck typically lies in the singular value or eigenvalue decompositions involved in the renormalization step. This is particularly true on GPUs, where tensor contractions are substantially faster than these decompositions. Here we propose a contraction scheme for C4vC_{4v}-symmetric tensor networks based on combining the corner transfer matrix renormalization group (CTMRG) with QR-decompositions which are substantially faster -- especially on GPUs. Our approach achieves up to two orders of magnitude speedup compared to standard CTMRG and yields state-of-the-art results for the Heisenberg and J1J_1-J2J_2 models in about one hour on an H100 GPU.

Simplified Fermionic Scattering State Preparation for the NISQ Era

Authors: Michael Hite

arXiv ID: 2505.00476 | Date: 2025-05-01

Abstract: With quantum computers steadily improving, large volume quantum scattering simulations is getting very close. Yet, in the noisy intermediate scale quantum (NISQ) era, we are limited to shallow circuits on the order of a thousand layers. Thus, accurate and efficient state preparation methods are needed. We introduce a simplified fermionic scattering state preparation method that reduces circuit depth significantly by partially relaxing the fermionic condition. Using the 1+1D transverse field Ising model as our test bed with exact diagonalization and time evolving block decimation with matrix product states, we show that our simplified states retain nearly all of the behavior of the true fermionic state while being prepared on just a handful of qubits. We also show promising early results on IonQ Forte 1.

Tree tensor network hierarchical equations of motion based on time-dependent variational principle for efficient open quantum dynamics in structured thermal environments

Authors: Xinxian Chen, Ignacio Franco

arXiv ID: 2505.00126 | Date: 2025-04-30

Abstract: We introduce an efficient method TTN-HEOM for exactly calculating the open quantum dynamics for driven quantum systems interacting with highly structured bosonic baths by combining the tree tensor network (TTN) decomposition scheme to the bexcitonic generalization of the numerically-exact hierarchical equations of motion (HEOM). The method yields a series of quantum master equations for all core tensors in the TTN that efficiently and accurately capture the open quantum dynamics for non-Markovian environments to all orders in the system-bath interaction. These master equations are constructed based on the time-dependent Dirac--Frenkel variational principle which isolates the optimal dynamics for the core tensors given the TTN ansatz. The dynamics converges to the HEOM when increasing the rank of the core tensors, a limit in which the TTN ansatz becomes exact. We introduce TENSO, Tensor Equations for Non-Markovian Structured Open systems, as a general-purpose Python code to propagate the TTN-HEOM dynamics. We implement three general propagators for the coupled master equations: Two fixed-rank methods that require a constant memory footprint during the dynamics, and one adaptive-rank method with variable memory footprint controlled by the target level of computational error. We exemplify the utility of these methods by simulating a two-level system coupled to a structured bath containing one Drude--Lorentz component and eight Brownian oscillators, which is beyond what can presently be computed using the standard HEOM. Our results show that the TTN-HEOM is capable to simulate both dephasing and relaxation dynamics of driven quantum system interacting with structured baths, even those of chemical complexity, with affordable computational cost.

Contemporary tensor network approaches to gapless and topological phases in an extended Bose-Hubbard ladder

Authors: Yuma Watanabe, Ravindra W. Chhajlany, Maciej Lewenstein, Tobias Graß, Utso Bhattacharya

arXiv ID: 2505.00106 | Date: 2025-04-30

Abstract: The development of numerically efficient computational methods has facilitated in depth studies of various correlated phases of matter including critical and topological phases. A quantum Monte-Carlo study of an extended Bose-Hubbard ladder has recently been used to identify an exotic phase with hidden order, where superfluid correlations coexist with string order, dubbed a Haldane superfluid (HSF). However, finite-size methods can struggle to uniquely determine the boundaries of quasi-long-range ordered states with nonlocal, e.g. string-like, correlations. In the present Letter, we revisit the HSF scenario using tensor network algorithms specialized for finite/infinite (quasi-)1D systems, \textit{i.e.} the well-governed finite-size density matrix renormalization group (DMRG), and the state-of-the-art infinite-size variational uniform matrix product state (VUMPS) methods. While DMRG results extrapolated to the thermodynamic limit are compatible with a putative HSF, the results from the VUMPS calculations provide sharper phase boundaries that leave no room for such a topological superfluid. Our results demonstrate the crucial advantage of the VUMPS in characterizing topological and critical interacting phases providing the precise phase boundaries.

An unbiased measure over the matrix product state manifold

Authors: Sebastian Leontica, Andrew G. Green

arXiv ID: 2505.00073 | Date: 2025-04-30

Abstract: Matrix product states are useful representations for a large variety of naturally occurring quantum states. Studying their typical properties is important for understanding universal behavior, including quantum chaos and thermalization, as well as the limits of classical simulations of quantum devices. We show that the usual ensemble of sequentially generated random matrix product states (RMPS) using local Haar random unitaries is not uniform when viewed as a restriction of the full Hilbert space. As a result, the entanglement across the chain exhibits an anomalous asymmetry under spatial inversion. We show how to construct an unbiased measure starting from the left-canonical form and design a Metropolis algorithm for sampling random states. Some properties of this new ensemble are investigated both analytically and numerically, such as the resulting resolution of identity over matrix product states and the typical entanglement spectrum, which is found to differ from the sequentially generated case.

An Optimally Accurate Lanczos Algorithm in the Matrix Product State Representation

Authors: Yu Wang, Zhangyu Yang, Xingyao Wu, Christian B. Mendl

arXiv ID: 2504.21786 | Date: 2025-04-30

Abstract: We improve the convergence of the Lanczos algorithm using the matrix product state representation. As an alternative to the density matrix renormalization group (DMRG), the Lanczos algorithm avoids local minima and can directly find multiple low-lying eigenstates. However, its performance and accuracy are affected by the truncation required to maintain the efficiency of the tensor network representation. In this work, we propose the modified thick-block Lanczos method to enhance the convergence of the Lanczos algorithm with MPS representation. We benchmark our method on one-dimensional instances of the Fermi-Hubbard model and the Heisenberg model in an external field, using numerical experiments targeting the first five lowest eigenstates. Across these tests, our approach attains the best possible accuracy permitted by the given bond dimension. This work establishes the Lanczos method as a reliable and accurate framework for finding multiple low-lying states within a tensor-network representation

Universal Structures and Emergent Geometry from Large-cc BCFT Ensemble

Authors: Ling-Yan Hung, Yikun Jiang, Bing-Xin Lao

arXiv ID: 2504.21660 | Date: 2025-04-30

Abstract: In this paper, we study the ensemble average of boundary CFT (BCFT) data consistent with the bootstrap equations. We apply the results to computing ensemble average of copies of multi-point correlation functions of boundary changing operators (BCO), and find the results in agreement with one copy of the Virasoro TQFT. Further, we consider ensemble average of CFT path-integrals expressed as tensor networks of BCO correlation functions using the formalism developed in arXiv:2210.12127, arXiv:2311.18005 and arXiv:2403.03179. We find a natural emergence of locality and a loop-sum structure reminiscent of lattice integrable models. We illustrate this universal structure through explicit examples at genus zero and genus one. Moreover, we provide strong evidence that, at leading order in large-cc, the results match those of three-dimensional Einstein gravity. In the presence of closed CFT operator insertions, generalized free fields emerge, with their correlation functions governed by the shortest paths connecting the insertions.

Superconductivity and trimers on attractive-UU Hubbard ladders

Authors: Ian Pilé, Evgeni Burovski

arXiv ID: 2504.21630 | Date: 2025-04-30

Abstract: We investigate the interplay between superconducting correlations and trimer formation in polarized two-component Fermi gases confined to multileg attractive-UU Hubbard ladders. Employing density matrix renormalization group (DMRG) simulations, we explore the effects of spin-dependent tunneling amplitudes on these systems. Specifically, we analyze how bound states of three fermions (trimers) impact Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconducting correlations at commensurate charge carrier densities, where 2n=n2n_{\uparrow} = n_{\downarrow}. In one-dimensional (1D) systems, trimer formation is known to suppress FFLO correlations exponentially. Our results demonstrate that this suppression persists on ladder lattices of small width, effectively mirroring the 1D behavior. However, we find a striking departure from the 1D regime as the ladder width increases. On ladders with a width of four legs, the influence of trimers on superconducting correlations becomes negligible, suggesting that wider ladder systems provide a distinct environment where FFLO-like pairing remains robust even in the presence of trimer states. These findings underscore the dimensional crossover in Hubbard systems and shed light on the mechanisms governing superconductivity and bound-state formation in strongly correlated fermionic systems. Our work has implications for understanding unconventional superconductivity in strongly correlated systems.

Discrete time crystals detected by time-translation twist

Authors: Ryota Nakai, Taozhi Guo, Shinsei Ryu

arXiv ID: 2504.21461 | Date: 2025-04-30

Abstract: We introduce a boundary condition twisted by time translation as a novel probe to characterize dynamical phases in periodically driven (Floquet) quantum systems. Inspired by twisted boundary conditions in equilibrium systems, this approach modifies the temporal evolution of the system upon completing a spatial loop, enabling the identification of distinct Floquet phases, including discrete time crystals (DTCs). By studying the spectral form factor (SFF) and its response to the twist, we uncover signatures of time-crystalline order, which exhibits periodic dependence on the twist parameter analogous to the Little-Parks effect in superconductors. We apply this framework to the kicked Ising model, demonstrating that our twist can distinguish time-crystalline phases.

A Unified Variational Framework for Quantum Excited States

Authors: Shi-Xin Zhang, Lei Wang

arXiv ID: 2504.21459 | Date: 2025-04-30

Abstract: Determining quantum excited states is crucial across physics and chemistry but presents significant challenges for variational methods, primarily due to the need to enforce orthogonality to lower-energy states, often requiring state-specific optimization, penalty terms, or specialized ansatz constructions. We introduce a novel variational principle that overcomes these limitations, enabling the \textit{simultaneous} determination of multiple low-energy excited states. The principle is based on minimizing the trace of the inverse overlap matrix multiplied by the Hamiltonian matrix, Tr(S1H)\mathrm{Tr}(\mathbf{S}^{-1}\mathbf{H}), constructed from a set of \textit{non-orthogonal} variational states {ψi}\{|ψ_i\rangle\}. Here, Hij=ψiHψj\mathbf{H}_{ij} = \langleψ_i | H | ψ_j\rangle and Sij=ψiψj\mathbf{S}_{ij} = \langleψ_i | ψ_j\rangle are the elements of the Hamiltonian and overlap matrices, respectively. This approach variationally optimizes the entire low-energy subspace spanned by {ψi}\{|ψ_i\rangle\} without explicit orthogonality constraints or penalty functions. We demonstrate the power and generality of this method across diverse physical systems and variational ansatzes: calculating the low-energy spectrum of 1D Heisenberg spin chains using matrix product states, finding vibrational spectrum of Morse potential using quantics tensor trains for real-space wavefunctions, and determining excited states for 2D fermionic Hubbard model with variational quantum circuits. In all applications, the method accurately and simultaneously obtains multiple lowest-lying energy levels and their corresponding states, showcasing its potential as a unified and flexible framework for calculating excited states on both classical and quantum computational platforms.

Preparation Circuits for Matrix Product States by Classical Variational Disentanglement

Authors: Refik Mansuroglu, Norbert Schuch

arXiv ID: 2504.21298 | Date: 2025-04-30

Abstract: We study the classical compilation of quantum circuits for the preparation of matrix product states (MPS), which are quantum states of low entanglement with an efficient classical description. Our algorithm represents a near-term alternative to previous sequential approaches by reverse application of a disentangler, which can be found by minimizing bipartite entanglement measures after the application of a layer of parameterized disentangling gates. Since a successful disentangler is expected to decrease the bond dimension on average, such a layer-by-layer optimization remains classically efficient even for deep circuits. Additionally, as the Schmidt coefficients of all bonds are locally accessible through the canonical ΓΓ-ΛΛ form of an MPS, the optimization algorithm can be heavily parallelized. We discuss guarantees and limitations to trainability and show numerical results for ground states of one-dimensional, local Hamiltonians as well as artificially spread out entanglement among multiple qubits using error correcting codes.

TT-LoRA MoE: Unifying Parameter-Efficient Fine-Tuning and Sparse Mixture-of-Experts

Authors: Pradip Kunwar, Minh N. Vu, Maanak Gupta, Mahmoud Abdelsalam, Manish Bhattarai

arXiv ID: 2504.21190 | Date: 2025-04-29

Abstract: We propose Tensor-Trained Low-Rank Adaptation Mixture of Experts (TT-LoRA MoE), a novel computational framework integrating Parameter-Efficient Fine-Tuning (PEFT) with sparse MoE routing to address scalability challenges in large model deployments. Unlike traditional MoE approaches, which face substantial computational overhead as expert counts grow, TT-LoRA MoE decomposes training into two distinct, optimized stages. First, we independently train lightweight, tensorized low-rank adapters (TT-LoRA experts), each specialized for specific tasks. Subsequently, these expert adapters remain frozen, eliminating inter-task interference and catastrophic forgetting in multi-task setting. A sparse MoE router, trained separately, dynamically leverages base model representations to select exactly one specialized adapter per input at inference time, automating expert selection without explicit task specification. Comprehensive experiments confirm our architecture retains the memory efficiency of low-rank adapters, seamlessly scales to large expert pools, and achieves robust task-level optimization. This structured decoupling significantly enhances computational efficiency and flexibility: uses only 2% of LoRA, 0.3% of Adapters and 0.03% of AdapterFusion parameters and outperforms AdapterFusion by 4 value in multi-tasking, enabling practical and scalable multi-task inference deployments.

Extracting average properties of disordered spin chains with translationally invariant tensor networks

Authors: Kevin Vervoort, Wei Tang, Nick Bultinck

arXiv ID: 2504.21089 | Date: 2025-04-29

Abstract: We develop a tensor network-based method for calculating disorder-averaged expectation values in random spin chains without having to explicitly sample over disorder configurations. The algorithm exploits statistical translation invariance and works directly in the thermodynamic limit. We benchmark our method on the infinite-randomness critical point of the random transverse field Ising model.

Trotterization is substantially efficient for low-energy states

Authors: Kaoru Mizuta, Tomotaka Kuwahara

arXiv ID: 2504.20746 | Date: 2025-04-29

Abstract: Trotterization is one of the central approaches for simulating quantum many-body dynamics on quantum computers or tensor networks. In addition to its simple implementation, recent studies have revealed that its error and cost can be reduced if the initial state is closed in the low-energy subspace. However, the improvement by the low-energy property rapidly vanishes as the Trotter order grows in the previous studies, and thus, it is mysterious whether there exists genuine advantage of low-energy initial states. In this Letter, we resolve this problem by proving the optimal error bound and cost of Trotterization for low-energy initial states. For generic local Hamiltonians composed of positive-semidefinite terms, we show that the Trotter error is at most linear in the initial state energy ΔΔ and polylogarithmic in the system size NN. As a result, the computational cost becomes substantially small for low-energy states with Δo(Ng)Δ\in o(Ng) compared to the one for arbitrary initial states, where gg denotes the energy per site and NgNg means the whole-system energy. Our error bound and cost of Trotterization achieve the theoretically-best scaling in the initial state energy ΔΔ. In addition, they can be partially extended to weakly-correlated initial states having low-energy expectation values, which are not necessarily closed in the low-energy subspace. Our results will pave the way for fast and accurate simulation of low-energy states, which are one central targets in condensed matter physics and quantum chemistry.

Hamiltonian Learning of Triplon Excitations in an Artificial Nanoscale Molecular Quantum Magnet

Authors: Rouven Koch, Robert Drost, Peter Liljeroth, Jose L. Lado

arXiv ID: 2504.20711 | Date: 2025-04-29

Abstract: Extracting the Hamiltonian parameters of nanoscale quantum magnets from experimental measurements is a significant challenge in quantum matter. Here we establish a machine learning strategy to extract the parameters of a spin Hamiltonian from inelastic spectroscopy with scanning tunneling microscopy, and we demonstrate this methodology experimentally with an artificial nanoscale molecular magnet based on cobalt phthalocyanine (CoPC) molecules on NbSe2_2. We show that this technique allows us to extract the Hamiltonian parameters of a quantum magnet from the differential conductance, including the substrate-induced spatial variation of the exchange couplings. Our methodology leverages a machine learning algorithm trained on exact quantum many-body simulations with tensor networks of finite quantum magnets, leading to a methodology that predicts the Hamiltonian parameters of CoPC quantum magnets of arbitrary size. Our results demonstrate how quantum many-body methods and machine learning enable us to learn a microscopic description of nanoscale quantum many-body systems with scanning tunneling spectroscopy.

Non-stabilizerness generation in a multi-particle quantum walk

Authors: Cătălin Paşcu Moca, Doru Sticlet, Balázs Dóra, Angelo Valli, Dominik Szombathy, Gergely Zaránd

arXiv ID: 2504.19750 | Date: 2025-04-28

Abstract: We investigate the generation of non-stabilizerness, or magic, in a multi-particle quantum walk by analyzing the time evolution of the stabilizer Rényi entropy M2M_2. Our study considers both single- and two-particle quantum walks in the framework of the XXZ Heisenberg model with varying interaction strengths. We demonstrate that the spread of magic follows the light-cone structure dictated by the system's dynamics, with distinct behaviors emerging in the easy-plane (Δ<1Δ< 1) and easy-axis (Δ>1Δ> 1) regimes. For Δ<1Δ< 1, magic generation is primarily governed by single-particle dynamics, while for Δ>1Δ> 1, doublon propagation dominates, resulting in a significantly slower growth of M2M_2. Furthermore, the magic exhibits logarithmic growth in time for both one and two-particle dynamics. Additionally, by examining the Pauli spectrum, we show that the statistical distribution of level spacings exhibits Poissonian behavior, independent of interaction strength or particle number. Our results shed light on the role of interactions on magic generation in a many-body system.

Classical simulation of parity-preserving quantum circuits

Authors: Carolin Wille, Sergii Strelchuk

arXiv ID: 2504.19317 | Date: 2025-04-27

Abstract: We present a classical simulation method for fermionic quantum systems which, without loss of generality, can be represented by parity-preserving circuits made of two-qubit gates in a brick-wall structure. We map such circuits to a fermionic tensor network and introduce a novel decomposition of non-Matchgate gates into a Gaussian fermionic tensor and a residual quartic term, inspired by interacting fermionic systems. The quartic term is independent of the specific gate, which allows us to precompute intermediate results independently of the exact circuit structure and leads to significant speedups when compared to other methods. Our decomposition suggests a natural perturbative expansion which can be turned into an algorithm to compute measurement outcomes and observables to finite accuracy when truncating at some order of the expansion. For particle number conserving gates, our decomposition features a unique truncation cutoff reducing the computational effort for high precision calculations. Our algorithm significantly lowers resource requirements for simulating parity-preserving circuits while retaining high accuracy, making it suitable for simulations of interacting systems in quantum chemistry and material science. Lastly, we discuss how our algorithm compares to other classical simulation methods for fermionic quantum systems.

On Ising model in magnetic field on the lattice

Authors: Raghav G. Jha

arXiv ID: 2504.18744 | Date: 2025-04-25

Abstract: We conjecture an approximate expression for the free energy in the thermodynamic limit of the classical square lattice Ising model in a uniform (real) magnetic field. The zero-field result is well known due to Onsager for more than eighty years, but no such result exists for a nonzero magnetic field on a regular lattice. We verify our conjecture using numerical tensor renormalization group (TRG) methods and find good agreement with a maximum deviation of 2%\sim2\% from the numerical results for the free energy across all ββ and real magnetic field, hh.

Micromagnons and long-range entanglement in ferrimagnetic ground states

Authors: Marcin Wieśniak, Ankit Kumar, Idriss Hank Nkouatchoua Ngueya

arXiv ID: 2504.18724 | Date: 2025-04-25

Abstract: While significant attention has been devoted to studying entanglement in photonic systems, solid-state spin lattices remain relatively underexplored. Motivated by this gap, we investigate the entanglement structure of one-dimensional ferrimagnetic chains composed of alternating spin-1/2 and spin-3/2 particles. We characterize the ground-state correlations using exact diagonalization and the Density Matrix Renormalization Group method. Although the bipartite entanglement is restricted to nearest neighbors, we reveal the presence of long-range genuine multipartite entanglement between spatially separated spin pairs. These findings advance our understanding of quantum correlations in ferrimagnetic materials.

Efficient witnessing and testing of magic in mixed quantum states

Authors: Tobias Haug, Poetri Sonya Tarabunga

arXiv ID: 2504.18098 | Date: 2025-04-25

Abstract: Nonstabilizerness or `magic' is a crucial resource for quantum computers which can be distilled from noisy quantum states. However, determining the magic of mixed quantum has been a notoriously difficult task. Here, we provide efficient witnesses of magic based on the stabilizer Rényi entropy which robustly indicate the presence of magic and quantitatively estimate magic monotones. We also design efficient property testing algorithms to reliably distinguish states with high and low magic, assuming the entropy is bounded. We apply our methods to certify the number of noisy T-gates under a wide class of noise models. Additionally, using the IonQ quantum computer, we experimentally verify the magic of noisy random quantum circuits. Surprisingly, we find that magic is highly robust, persisting even under exponentially strong noise. Our witnesses can also be efficiently computed for matrix product states, revealing that subsystems of many-body quantum states can contain extensive magic despite entanglement. Finally, our work also has direct implications for cryptography and pseudomagic: To mimic high magic states with as little magic as possible, one requires an extensive amount of entropy. This implies that entropy is a necessary resource to hide magic from eavesdroppers. Our work uncovers powerful tools to verify and study the complexity of noisy quantum systems.

Quantum State Design and Emergent Confinement Mechanism in Measured Tensor Network States

Authors: Guglielmo Lami, Andrea De Luca, Xhek Turkeshi, Jacopo De Nardis

arXiv ID: 2504.16995 | Date: 2025-04-23

Abstract: Randomness is a fundamental aspect of quantum mechanics, arising from the measurement process that collapses superpositions into definite outcomes according to Born's rule. Generating large-scale random quantum states is crucial for quantum computing and many-body physics, yet remains a key challenge. We present a practical method based on local measurements of random Tensor Networks, focusing on random Matrix Product States (MPS) generated by two distinct quantum circuit architectures, both feasible on near-term devices. We certify the emergent quantum randomness using the frame potential and establish a mapping between its behavior and the statistical mechanics of a domain wall particle model. In both architectures, the effect of quantum measurements induces a nontrivial confinement mechanism, where domain walls are either trapped by an external potential or bound in pairs to form meson-like excitations. Our results, supported by both exact analytical calculations and numerical simulations, suggest that confinement is a general mechanism underlying random state generation in broader settings with local measurements, including quantum circuits and chaotic dynamics.

Anomalous matrix product operator symmetries and 1D mixed-state phases

Authors: Xiao-Qi Sun

arXiv ID: 2504.16985 | Date: 2025-04-23

Abstract: Generalized symmetries have emerged as a powerful organizing principle for exotic quantum phases. However, their role in open quantum systems, especially for non-invertible cases, remains largely unexplored. We address this by applying a unified tensor-network framework for mixed states with fusion categorical symmetry, which encompasses both invertible and non-invertible ones represented as matrix product operators, and reveals novel quantum phases unique to the open-system setting through the lens of quantum anomalies. In contrast to pure states, where anomalies forbid symmetric short-range correlated phases in one dimension, we construct a broad class of renormalization fixed-point mixed states with zero correlation length given arbitrary strong anomalous fusion categorical symmetry. These states, representing nontrivial mixed-state phases of matter, cannot be efficient prepared via local quantum channels, indicating anomaly-enforced long-range entanglement in the absence of local correlations. Despite this obstruction, we further provide constructions of measurement-enhanced quantum circuits to prepare all these constructed states, offering a practical way to realize and probe anomalous generalized symmetries in open quantum systems.

Simulating Quantum Circuits with Tree Tensor Networks using Density-Matrix Renormalization Group Algorithm

Authors: Aditya Dubey, Zeki Zeybek, Peter Schmelcher

arXiv ID: 2504.16718 | Date: 2025-04-23

Abstract: Quantum computing offers the potential for computational abilities that can go beyond classical machines. However, they are still limited by several challenges such as noise, decoherence, and gate errors. As a result, efficient classical simulation of quantum circuits is vital not only for validating and benchmarking quantum hardware but also for gaining deeper insights into the behavior of quantum algorithms. A promising framework for classical simulation is provided by tensor networks. Recently, the Density-Matrix Renormalization Group (DMRG) algorithm was developed for simulating quantum circuits using matrix product states (MPS). Although MPS is efficient for representing quantum states with one-dimensional correlation structures, the fixed linear geometry restricts the expressive power of the MPS. In this work, we extend the DMRG algorithm for simulating quantum circuits to tree tensor networks (TTNs). The framework employs a variational compression scheme that optimizes the TTN to approximate the evolved quantum state. To benchmark the method, we simulate random circuits and the quantum approximate optimization algorithm (QAOA) with various two-qubit gate connectivities. For the random circuits, we devise tree-like gate layouts that are suitable for TTN and show that TTN requires less memory than MPS for the simulations. For the QAOA circuits, a naive TTN construction that exploits graph structure significantly improves the simulation fidelities. Our findings show that the DMRG algorithm with TTNs provides a promising framework for simulating quantum circuits, particularly when gate connectivities exhibit clustering or a hierarchical structure.

Exact steady states and fragmentation-induced relaxation in the no-passing asymmetric simple exclusion process

Authors: Urei Miura

arXiv ID: 2504.16363 | Date: 2025-04-23

Abstract: We introduce a multi-species generalization of the asymmetric simple exclusion process (ASEP) with a ``no-passing" constraint, forbidding overtaking, on a one-dimensional open chain. This no-passing rule fragments the Hilbert space into an exponential number of disjoint sectors labeled by the particle sequence, leading to relaxation dynamics that depend sensitively on the initial ordering. We construct exact matrix-product steady states in every particle sequence sector and derive closed-form expressions for the particle-number distribution and two-point particle correlation functions. In the two-species case, we identify a parameter regime where some sectors relax in finite time while others exhibit metastable relaxation dynamics, revealing the coexistence of fast and slow dynamics and strong particle sequence sector dependence. Our results uncover a novel mechanism for non-equilibrium metastability arising from Hilbert space fragmentation in exclusion processes.

Nontrivial entanglement passively mediated by a quenched magnetic impurity

Authors: Adelina A. Orlandini, Germán G. Blesio, Claudio J. Gazza, Luis O. Manuel

arXiv ID: 2504.16308 | Date: 2025-04-22

Abstract: We investigate the entanglement properties of a Kondo system undergoing a transition to a state with a quenched magnetic impurity, using the density matrix renormalization group (DMRG) method. We focus on a two-channel spin-1 Kondo impurity with single-ion anisotropy, where a quantum phase transition occurs between two topologically distinct local Fermi liquids. In the fully screened Kondo phase, realized at lower anisotropies, the entangled region surrounding the magnetic impurity mimics the Kondo screening cloud, although its length does not follow the conventional behavior. In contrast, beyond the transition, the system enters a non-Landau Fermi liquid phase with a markedly different entanglement structure: as the impurity is quenched and disentangled from the rest of the system due to the breakdown of the Kondo effect, the two conduction channels coupled only through the impurity develop a significant degree of entanglement with one another. Our findings demonstrate that a quenched magnetic impurity can passively and efficiently mediate entanglement between spatially separated conduction bands.

Augmenting Simulated Noisy Quantum Data Collection by Orders of Magnitude Using Pre-Trajectory Sampling with Batched Execution

Authors: Taylor L. Patti, Thien Nguyen, Justin G. Lietz, Alexander J. McCaskey, Brucek Khailany

arXiv ID: 2504.16297 | Date: 2025-04-22

Abstract: Classically simulating quantum systems is challenging, as even noiseless nn-qubit quantum states scale as 2n2^n. The complexity of noisy quantum systems is even greater, requiring 2n×2n2^n \times 2^n-dimensional density matrices. Various approximations reduce density matrix overhead, including quantum trajectory-based methods, which instead use an ensemble of m2nm \ll 2^n noisy states. While this method is dramatically more efficient, current implementations use unoptimized sampling, redundant state preparation, and single-shot data collection. In this manuscript, we present the Pre-Trajectory Sampling technique, increasing the efficiency and utility of trajectory simulations by tailoring error types, batching sampling without redundant computation, and collecting error information. We demonstrate the effectiveness of our method with both a mature statevector simulation of a 35-qubit quantum error-correction code and a preliminary tensor network simulation of 85 qubits, yielding speedups of up to 10610^6x and 1616x, as well as generating massive datasets of one trillion and one million shots, respectively.

Kronecker states: a powerful source of multipartite maximally entangled states in quantum information

Authors: Walther Gonzalez

arXiv ID: 2504.16256 | Date: 2025-04-22

Abstract: In quantum information theory, maximally entangled states, specifically locally maximally entangled (LME) states, are essential for quantum protocols. While many focus on bipartite entanglement, applications such as quantum error correction and multiparty secret sharing rely on multipartite entanglement. These LME states naturally appear in the invariant subspaces of tensor products of irreducible representations of the symmetric group SnS_n, called Kronecker subspaces, whose dimensions are the Kronecker coefficients. A Kronecker subspace is a space of multipartite LME states that entangle high-dimensional Hilbert spaces. Although these states can be derived from Clebsch-Gordan coefficients of SnS_n, known methods are inefficient even for small nn. A quantum-information-based alternative comes from entanglement concentration protocols, where Kronecker subspaces arise in the isotypic decomposition of multiple copies of entangled states. Closed forms have been found for the multiqubit WW-class states, but not in general. This thesis extends that approach to any multiqubit system. We first propose a graphical construction called W-state Stitching, where multiqubit entangled states are represented as tensor networks built from WW states. By analyzing the isotypic decomposition of copies of these graph states, corresponding graph Kronecker states can be constructed. In particular, graph states of generic multiqubit systems can generate any Kronecker subspace. We explicitly construct bases for three- and four-qubit systems and show that the W-stitching technique also serves as a valuable tool for multiqubit entanglement classification. These results may open new directions in multipartite entanglement resource theories, with bipartite and tripartite WW states as foundational elements, and asymptotic analysis based on Kronecker states.

Robust Mixed-State Cluster States and Spurious Topological Entanglement Negativity

Authors: Seunghun Lee, Eun-Gook Moon

arXiv ID: 2504.16165 | Date: 2025-04-22

Abstract: We investigate 1D and 2D cluster states under local decoherence to assess the robustness of their mixed-state subsystem symmetry-protected topological (SSPT) order. By exactly computing fidelity correlators via dimensional reduction of effective statistical mechanics models, we pinpoint the critical error rate for strong-to-weak spontaneous breaking of strong subsystem symmetry. Without resorting to the replica trick, we demonstrate that mixed-state SSPT order remains remarkably robust up to the maximal decoherence rate when noise respects strong subsystem symmetry. Furthermore, we propose that the mixed-state SSPT order can be detected by a constant correction to the area-law scaling of entanglement negativity, termed spurious topological entanglement negativity. This also highlights that topological entanglement negativity, a widely used diagnostic for mixed-state topological order, is generally not invariant under finite-depth quantum channels.

Multi-Scale Tensorial Summation and Dimensional Reduction Guided Neural Network for Edge Detection

Authors: Lei Xu, Mehmet Yamac, Mete Ahishali, Moncef Gabbouj

arXiv ID: 2504.15770 | Date: 2025-04-22

Abstract: Edge detection has attracted considerable attention thanks to its exceptional ability to enhance performance in downstream computer vision tasks. In recent years, various deep learning methods have been explored for edge detection tasks resulting in a significant performance improvement compared to conventional computer vision algorithms. In neural networks, edge detection tasks require considerably large receptive fields to provide satisfactory performance. In a typical convolutional operation, such a large receptive field can be achieved by utilizing a significant number of consecutive layers, which yields deep network structures. Recently, a Multi-scale Tensorial Summation (MTS) factorization operator was presented, which can achieve very large receptive fields even from the initial layers. In this paper, we propose a novel MTS Dimensional Reduction (MTS-DR) module guided neural network, MTS-DR-Net, for the edge detection task. The MTS-DR-Net uses MTS layers, and corresponding MTS-DR blocks as a new backbone to remove redundant information initially. Such a dimensional reduction module enables the neural network to focus specifically on relevant information (i.e., necessary subspaces). Finally, a weight U-shaped refinement module follows MTS-DR blocks in the MTS-DR-Net. We conducted extensive experiments on two benchmark edge detection datasets: BSDS500 and BIPEDv2 to verify the effectiveness of our model. The implementation of the proposed MTS-DR-Net can be found at https://github.com/LeiXuAI/MTS-DR-Net.git.

Moment Tensor Potential and Equivariant Tensor Network Potential with explicit dispersion interactions

Authors: Olga Chalykh, Dmitry Korogod, Ivan S. Novikov, Max Hodapp, Nikita Rybin, Alexander V. Shapeev

arXiv ID: 2504.15760 | Date: 2025-04-22

Abstract: In this study, we investigate the effect of incorporating explicit dispersion interactions in the functional form of machine learning interatomic potentials (MLIPs), particularly in the Moment Tensor Potential and Equivariant Tensor Network potential for accurate modeling of liquid carbon tetrachloride, methane, and toluene. We show that explicit incorporation of dispersion interactions via D2 and D3 corrections significantly improves the accuracy of MLIPs when the cutoff radius is set to a commonly used value of 5 -- 6 Å. We also show that for carbon tetrachloride and methane, a substantial improvement in accuracy can be achieved by extending the cutoff radius to 7.5 Å. However, for accurate modeling of toluene, explicit incorporation of dispersion remains important. Furthermore, we find that MLIPs incorporating dispersion interactions via D2 reach a close level of accuracy to those incorporating D3, and D2 is suitable for accurate modeling of the systems in the study, while being less computationally expensive. We evaluated the accuracy of MLIPs in dimer binding curves compared to ab initio data and in predicting density and radial distribution functions compared to experiments.

Emergent Kitaev materials in synthetic Fermi-Hubbard bilayers

Authors: Daniel González-Cuadra, Alejandro Bermudez

arXiv ID: 2504.15755 | Date: 2025-04-22

Abstract: We investigate the emergence of bond-directional spin-spin interactions in a synthetic Fermi-Hubbard bilayer that can be realized with ultracold fermions in Raman optical lattices. The model exploits synthetic dimensions to couple two honeycomb layers, each corresponding to a different hyperfine atomic state, via Raman-assisted tunneling and, moreover, via an inter-layer Hubbard repulsion due to the cold-atom scattering. In the strong-coupling regime at half filling, we derive effective spin Hamiltonians for the kinetic exchange featuring Kitaev, Heisenberg, off-diagonal exchange (ΓΓ-couplings), as well as tunable Dzyaloshinskii-Moriya interactions. We identify specific configurations that generate both ferromagnetic and antiferromagnetic Kitaev couplings with various perturbations of relevance to Kitaev materials, providing a tunable platform that can explore how quantum spin liquids emerge from itinerant fermion systems. We analyze the Fermi-liquid and Mott-insulating phases, highlighting a correspondence between Dirac and Majorana quasi-particles, with possible phase transitions thereof. In an extreme anisotropic limit, we show that the model reduces to an inter-layer ribbon in a quasi-1D ladder, allowing for a numerical study of the correlated ground state using matrix product states. We find a transition from a symmetry-protected topological insulator to a Kitaev-like regime characterized by nonlocal string order. Our results establish that cold-atom quantum simulators based on Raman optical lattices can be a playground for extended Kitaev models, bridging itinerant fermionic systems and spin-liquid physics.

Derivatives of tree tensor networks and its applications in Runge--Kutta methods

Authors: Junyuan He, Zhonghao Sun, Jizu Huang

arXiv ID: 2504.15516 | Date: 2025-04-22

Abstract: Tree tensor networks (TTNs) provide a compact and structured representation of high-dimensional data, making them valuable in various areas of computational mathematics and physics. In this paper, we present a rigorous mathematical framework for expressing high-order derivatives of functional TTNs, both with or without constraints. Our framework decomposes the total derivative of a given TTN into a summation of TTNs, each corresponding to the partial derivatives of the original TTN. Using this decomposition, we derive the Taylor expansion of vector-valued functions subject to ordinary differential equation constraints or algebraic constraints imposed by Runge--Kutta (RK) methods. As a concrete application, we employ this framework to construct order conditions for RK methods. Due to the intrinsic tensor properties of partial derivatives and the separable tensor structure in RK methods, the Taylor expansion of numerical solutions can be obtained in a manner analogous to that of exact solutions using tensor operators. This enables the order conditions of RK methods to be established by directly comparing the Taylor expansions of the exact and numerical solutions, eliminating the need for mathematical induction. For a given function f\vec{f}, we derive sharper order conditions that go beyond the classical ones, enabling the identification of situations where a standard RK scheme of order {\it p} achieves unexpectedly higher convergence order for the particular function. These results establish new connections between tensor network theory and classical numerical methods, potentially opening new avenues for both analytical exploration and practical computation.

Branch-and-bound digitized counterdiabatic quantum optimization

Authors: Anton Simen, Sebastián V. Romero, Alejandro Gomez Cadavid, Enrique Solano, Narendra N. Hegade

arXiv ID: 2504.15367 | Date: 2025-04-21

Abstract: Branch-and-bound algorithms effectively solve combinatorial optimization problems, relying on the relaxation of the objective function to obtain tight lower bounds. While this is straightforward for convex objective functions, higher-order formulations pose challenges due to their inherent non-convexity. In this work, we propose branch-and-bound digitized counterdiabatic quantum optimization (BB-DCQO), a quantum algorithm that addresses the relaxation difficulties in higher-order unconstrained binary optimization (HUBO) problems. By employing bias fields as approximate solutions to the relaxed problem, we iteratively enhance the quality of the results compared to the bare bias-field digitized counterdiabatic quantum optimization (BF-DCQO) algorithm. We refer to this enhanced method as BBB-DCQO. In order to benchmark it against simulated annealing (SA), we apply it on sparse HUBO instances with up to 156156 qubits using tensor network simulations. To explore regimes that are less tractable for classical simulations, we experimentally apply BBB-DCQO to denser problems using up to 100 qubits on IBM quantum hardware. We compare our results with SA and a greedy-tuned quantum annealing baseline. In both simulations and experiments, BBB-DCQO consistently achieved higher-quality solutions with significantly reduced computational overhead, showcasing the effectiveness of integrating counterdiabatic quantum methods into branch-and-bound to address hard non-convex optimization tasks.

Note on Type III1III_1 Algebras in c=1c= 1 String Theory and Bulk Causal Diamonds

Authors: T. Banks

arXiv ID: 2504.15076 | Date: 2025-04-21

Abstract: We argue that the Leutheusser-Liu procedure of isolating a von Neumann algebra in the N=N = \infty limit of string theories, leads to the algebra of relativistic fermion fields on a half line for the c=1c = 1 string theory. This is a Type II von Neumann algebra, since it is the algebra of the Rindler wedge in the Rindler vacuum state. Subalgebras of finite regions are Type III1III_1. The argument uses the elegant results of Moore and of Alexandrov, Kazakov and Kostov. This model is well known to be integrable and have no black hole excitations. We have speculated that adding an interaction invisible in perturbation theory to a large finite number, MM, of copies of the model, produces a non-integrable model with meta-stable excitations having all of the properties of linear dilaton black holes. The algebra of fields is the tensor product of MM copies of the c=1c = 1 model's algebra, whether or not we add the non-integrable interaction. We argue that the infinite dimensional c=1c = 1 algebras are analogous to those of the boundary field theory in AdS/CFT, even though they appear to encode bulk causal structure. An IR cutoff on the boundary renders them finite and causal structure must be formulated in terms of an analog of the Tensor Network Renormalization Group. This is a time dependent Hamiltonian flow, embedding smaller Hilbert spaces into larger ones. It is the analog of one sided modular inclusion in quantum field theory.

Trainable Quantum Neural Network for Multiclass Image Classification with the Power of Pre-trained Tree Tensor Networks

Authors: Keisuke Murota, Takumi Kobori

arXiv ID: 2504.14995 | Date: 2025-04-21

Abstract: Tree tensor networks (TTNs) offer powerful models for image classification. While these TTN image classifiers already show excellent performance on classical hardware, embedding them into quantum neural networks (QNNs) may further improve the performance by leveraging quantum resources. However, embedding TTN classifiers into QNNs for multiclass classification remains challenging. Key obstacles are the highorder gate operations required for large bond dimensions and the mid-circuit postselection with exponentially low success rates necessary for the exact embedding. In this work, to address these challenges, we propose forest tensor network (FTN)-classifiers, which aggregate multiple small-bond-dimension TTNs. This allows us to handle multiclass classification without requiring large gates in the embedded circuits. We then remove the overhead of mid-circuit postselection by extending the adiabatic encoding framework to our setting and smoothly encode the FTN-classifiers into a quantum forest tensor network (qFTN)- classifiers. Numerical experiments on MNIST and CIFAR-10 demonstrate that we can successfully train FTN-classifiers and encode them into qFTN-classifiers, while maintaining or even improving the performance of the pre-trained FTN-classifiers. These results suggest that synergy between TTN classification models and QNNs can provide a robust and scalable framework for multiclass quantum-enhanced image classification.

Page curve like dynamics in Interacting Quantum Systems

Authors: Tamoghna Ray, Abhishek Dhar, Manas Kulkarni

arXiv ID: 2504.14675 | Date: 2025-04-20

Abstract: We study the dynamics of entanglement in a one-dimensional XXZXXZ spin-1/21/2 chain, with and without integrability-breaking interactions, that is connected to a bath. We start from a state where the system and bath are completely unentangled, and the bath is polarized spin-down. We consider two different initial states for the system - (i) a polarized spin-up state, and (ii) an infinite temperature state. In the particle representation of the spin chain, the polarized spin-up state corresponds to a filled state, while the polarized spin-down state corresponds to an empty state. Starting from these inhomogeneous quenches, in all the above-mentioned cases we obtain the Page curve like behavior in the entanglement. We report different power-law behavior in the growth of entanglement for different initial states and different kinds of baths (interacting and non-interacting). In an attempt to explore plausible deep connections between entanglement and Boltzmann entropy, we investigate the latter in both the filled and the infinite temperature case, for the system and the bath. For the filled case, the Boltzmann entropy of the system has the form of a Page curve but quantitatively deviates from the entanglement. On the other hand, the entropy of the bath keeps increasing. Remarkably, for the infinite temperature case, we find that the system and bath Boltzmann entropies agree with the entanglement entropy, after and before the Page time, respectively. Our findings are expected to hold for generic interacting quantum systems and could be of relevance to black hole physics.

Developments in the applications of density functional theory to fractional quantum Hall systems

Authors: Yi Yang, Yayun Hu, Zi-Xiang Hu

arXiv ID: 2504.14558 | Date: 2025-04-20

Abstract: The fractional quantum Hall effect remains a captivating area in condensed matter physics, characterized by strongly correlated topological order, which manifests as fractionalized excitations and anyonic statistics. Numerical simulations, such as exact diagonalization, density matrix renormalization group, matrix product states, and Monte Carlo methods, are essential to examine the properties of strongly correlated systems. Recently, density functional theory has been employed in this field within the framework of composite fermion theory. This paper systematically evaluates how density functional theory approaches have addressed fundamental challenges in fractional quantum Hall systems, including ground state and low-energy excitations. Special attention is given to the insights provided by density functional theory regarding composite fermion behavior, edge effects, and the nature of fractional charge and magnetoroton excitations. The discussion critically examines both the advantages and limitations of these approaches, while highlighting the productive interplay between numerical simulations and theoretical models. Future directions are explored, particularly the promising potential of time-dependent density functional theory for modeling non-equilibrium dynamics in quantum Hall systems.

Gauging Quantum Phases: A Matrix Product State Approach

Authors: David Blanik, José Garre-Rubio, Norbert Schuch

arXiv ID: 2504.14380 | Date: 2025-04-19

Abstract: Utilizing the framework of matrix product states, we investigate gauging as a method for exploring quantum phases of matter. Specifically, we describe how symmetry-protected topological (SPT) phases and spontaneous symmetry breaking (SSB) phases in one-dimensional spin systems behave under twisted gauging, a generalization of the well-known gauging procedure for globally symmetric states. Compared to previous, order parameter-based, approaches our analysis is not limited to the case of maximally non-commutative (MNC) phases and we use our findings to propose a generalization of the Kennedy-Tasaki transformation to the non-MNC setting. A key result of our work is that gauging produces configurations characterized by a combination of MNC order and symmetry breaking, when applied to non-MNC SPT phases. More generally, we conjecture a precise correspondence between SSB and non-MNC SPT phases, possibly enabling the detection of such phases using local and string order parameters.

Comparative Benchmarking of Utility-Scale Quantum Emulators

Authors: Anna Leonteva, Guido Masella, Maxime Outteryck, Asier Piñeiro Orioli, Shannon Whitlock

arXiv ID: 2504.14027 | Date: 2025-04-18

Abstract: Evaluating quantum algorithms at utility-scale - involving more than 100 qubits - is a key step toward advancing real-world applications of quantum computing. In this study, we benchmark seven state-of-the-art quantum emulators employing techniques such as tensor networks, matrix product states (MPS), decision diagrams, and factorized ket based methods, running on CPU based hardware and focusing on effectively exact simulations. Performance is assessed on 13 benchmark circuits from the MQTBench library, spanning circuit sizes from 4 to 1,024 qubits. Our results reveal that MPS-based emulators outperform other approaches overall, successfully solving 8 benchmarks up to the maximum size of 1,024 qubits and 12 benchmarks up to at least 100 qubits in less than 5 minutes. We find evidence that all circuits except a random one can be simulated in polynomial time. This work demonstrates that quantum emulators can faithfully simulate a broad range of large and complex universal quantum circuits with high fidelity, far beyond the limits of statevector simulators and today's quantum hardware.

Metrology of open quantum systems from emitted radiation

Authors: Siddhant Midha, Sarang Gopalakrishnan

arXiv ID: 2504.13815 | Date: 2025-04-18

Abstract: We explore the task of learning about the dynamics of a Markovian open quantum system by monitoring the information it radiates into its environment. For an open system with Hilbert space dimension DD, the quantum state of the emitted radiation can be described as a temporally ordered matrix-product state (MPS). We provide simple analytical expressions for the quantum Fisher information (QFI) of the radiation state, which asymptotically scales linearly with the sensing time unless the open system has multiple steady states. We characterize the crossovers in QFI near dynamical phase transitions, emphasizing the role of temporal correlations in setting the asymptotic rate at which QFI increases. We discuss when optimal sensing is possible with instantaneously measured radiation.

Realizing string breaking dynamics in a Z2Z_2 lattice gauge theory on quantum hardware

Authors: Constantia Alexandrou, Andreas Athenodorou, Kostas Blekos, Georgios Polykratis, Stefan Kühn

arXiv ID: 2504.13760 | Date: 2025-04-18

Abstract: We investigate static and dynamical aspects of string breaking in a Z2Z_2 lattice gauge theory coupled to Kogut-Susskind staggered fermions. Using Tensor Network simulations, we demonstrate that the static potential as well as the site-resolved configuration of the matter sites and gauge links allows us to identify the regimes in which string breaking occurs. Furthermore, we develop a variational quantum eigensolver that allows for reliably preparing the ground state of the theory in both the absence and presence of static charges and to capture the static aspects of the phenomenon. Carrying out state preparation on real quantum hardware for up to 19 qubits, we demonstrate its suitability for current quantum devices. In addition, we study the real-time dynamics of a flux tube between two static charges using both Tensor Networks and quantum hardware. Using a trotterization for the time-evolution operator, we are able to show that the breaking process starts with the creation of charges inside the string. These eventually redistribute towards the static charges and screen them, which leads to the breaking of the flux tube.

Finding periodic orbits in projected quantum many-body dynamics

Authors: Elena Petrova, Marko Ljubotina, Gökhan Yalnız, Maksym Serbyn

arXiv ID: 2504.12472 | Date: 2025-04-16

Abstract: Describing general quantum many-body dynamics is a challenging task due to the exponential growth of the Hilbert space with system size. The time-dependent variational principle (TDVP) provides a powerful tool to tackle this task by projecting quantum evolution onto a classical dynamical system within a variational manifold. In classical systems, periodic orbits play a crucial role in understanding the structure of the phase space and the long-term behavior of the system. However, finding periodic orbits is generally difficult, and their existence and properties in generic TDVP dynamics over matrix product states have remained largely unexplored. In this work, we develop an algorithm to systematically identify and characterize periodic orbits in TDVP dynamics. Applying our method to the periodically kicked Ising model, we uncover both stable and unstable periodic orbits. We characterize the Kolmogorov-Arnold-Moser tori in the vicinity of stable periodic orbits and track the change of the periodic orbits as we modify the Hamiltonian parameters. We observe that periodic orbits exist at any value of the coupling constant between prethermal and fully thermalizing regimes, but their relevance to quantum dynamics and imprint on quantum eigenstates diminishes as the system leaves the prethermal regime. Our results demonstrate that periodic orbits provide valuable insights into the TDVP approximation of quantum many-body evolution and establish a closer connection between quantum and classical chaos.

A tensor network approach to sensing quantum light-matter interactions

Authors: Aiman Khan, Francesco Albarelli, Animesh Datta

arXiv ID: 2504.12399 | Date: 2025-04-16

Abstract: We present the fundamental limits to the precision of estimating parameters of a quantum matter system probed by light, even when some of the light is lost. This practically inevitable scenario leads to a tripartite quantum system of matter, and light -- detected and lost. Evaluating fundamental information theoretic quantities such as the quantum Fisher information of only the detected light was heretofore impossible. We succeed by expressing the final quantum state of the detected light as a matrix product operator. We apply our method to resonance fluorescence and pulsed spectroscopy. For both, we quantify the sub-optimality of continuous homodyning and photo-counting measurements in parameter estimation. For the latter, we find that single-photon Fock state pulses allow higher precision per photon than pulses of coherent states. Our method should be valuable in studies of quantum light-matter interactions, quantum light spectroscopy, quantum stochastic thermodynamics, and quantum clocks.

Learning transitions in classical Ising models and deformed toric codes

Authors: Malte Pütz, Samuel J. Garratt, Hidetoshi Nishimori, Simon Trebst, Guo-Yi Zhu

arXiv ID: 2504.12385 | Date: 2025-04-16

Abstract: Conditional probability distributions describe the effect of learning an initially unknown classical state through Bayesian inference. Here we demonstrate the existence of a learning transition, having signatures in the long distance behavior of conditional correlation functions, in the two-dimensional classical Ising model. This transition, which arises when learning local energy densities, extends all the way from the infinite-temperature paramagnetic state down to the thermal critical state. The intersection of the line of learning transitions and the thermal Ising transition is a novel tricritical point. Our model for learning also describes the effects of weak measurements on a family of quantum states which interpolate between the (topologically ordered) toric code and a trivial product state. Notably, the location of the above tricritical point implies that the quantum memory in the entire topological phase is robust to weak measurement, even when the initial state is arbitrarily close to the quantum phase transition separating topological and trivial phases. Our analysis uses a replica field theory combined with the renormalization group, and we chart out the phase diagram using a combination of tensor network and Monte Carlo techniques. Our methods can be extended to study the more general effects of learning on both classical and quantum states.

ScarFinder: a detector of optimal scar trajectories in quantum many-body dynamics

Authors: Jie Ren, Andrew Hallam, Lei Ying, Zlatko Papić

arXiv ID: 2504.12383 | Date: 2025-04-16

Abstract: Mechanisms that give rise to coherent quantum dynamics, such as quantum many-body scars, have recently attracted much interest as a way of controlling quantum chaos. However, identifying the presence of quantum scars in general many-body Hamiltonians remains an outstanding challenge. Here we introduce ScarFinder, a variational framework that reveals possible scar-like dynamics without prior knowledge of scar states or their algebraic structure. By iteratively evolving and projecting states within a low-entanglement variational manifold, ScarFinder isolates scarred trajectories by suppressing thermal contributions. We validate the method on the analytically tractable spin-1 XY model, recovering the known scar dynamics, as well as the mixed field Ising model, where we capture and generalize the initial conditions previously associated with ``weak thermalization''. We then apply the method to the PXP model of Rydberg atom arrays, efficiently characterizing its mixed phase space and finding a previously unknown trajectory with nearly-perfect revival dynamics in the thermodynamic limit. Our results establish ScarFinder as a powerful, model-agnostic tool for identifying and optimizing coherent dynamics in quantum many-body systems.

A Strong-Coupling-Limit Study on the Pairing Mechanism in the Pressurized La3_3Ni2_2O7_7

Authors: Jia-Heng Ji, Chen Lu, Zhi-Yan Shao, Zhiming Pan, Fan Yang, Congjun Wu

arXiv ID: 2504.12127 | Date: 2025-04-16

Abstract: Recently, the bilayer perovskite nickelate La3_3Ni2_2O7_7 has been reported to exhibit high-temperature superconductivity near 8080 K under a moderate pressure of about 1414GPa. To investigate the underlying pairing mechanism and symmetry in this complex system, we propose and analyze a mixed spin-11 and spin-12\frac{1}{2} bilayer tt-JJ model in the strong coupling regime. This model explicitly incorporates the crucial role of strong Hund's coupling, which favors the formation of local spin-triplet states from the two onsite EgE_g orbital electrons at half-filling. We further investigate the model using both slave-particle mean-field theory and the density matrix renormalization group method. Our simulation results reveal that the dominate pairing channel is the interlayer one in the 3dx2y23d_{x^2-y^2} orbital. The Hund's coupling is shown to enhance superconductivity within a reasonable physical range. Moreover, electron doping strengthens superconductivity by increasing carrier density; in contrast, hole doping weakens superconductivity. These findings offer critical insights into the unconventional superconductivity of pressurized La3_3Ni2_2O7_7 and underline the important role of orbital-selective behavior and Hund's rule.

Integrating Neural Networks and Tensor Networks for Computing Free Energy

Authors: Hanyan Cao, Yijia Wang, Feng Pan, Pan Zhang

arXiv ID: 2504.12037 | Date: 2025-04-16

Abstract: Computing free energy is a fundamental problem in statistical physics. Recently, two distinct methods have been developed and have demonstrated remarkable success: the tensor-network-based contraction method and the neural-network-based variational method. Tensor networks are accu?rate, but their application is often limited to low-dimensional systems due to the high computational complexity in high-dimensional systems. The neural network method applies to systems with general topology. However, as a variational method, it is not as accurate as tensor networks. In this work, we propose an integrated approach, tensor-network-based variational autoregressive networks (TNVAN), that leverages the strengths of both tensor networks and neural networks: combining the variational autoregressive neural network's ability to compute an upper bound on free energy and perform unbiased sampling from the variational distribution with the tensor network's power to accurately compute the partition function for small sub-systems, resulting in a robust method for precisely estimating free energy. To evaluate the proposed approach, we conducted numerical experiments on spin glass systems with various topologies, including two-dimensional lattices, fully connected graphs, and random graphs. Our numerical results demonstrate the superior accuracy of our method compared to existing approaches. In particular, it effectively handles systems with long-range interactions and leverages GPU efficiency without requiring singular value decomposition, indicating great potential in tackling statistical mechanics problems and simulating high-dimensional complex systems through both tensor networks and neural networks.

Assessing Tensor Network Quantum Emulators for Hamiltonian Simulation of Pharmaceutical Molecules: Challenges and Limitations in Drug Discovery Applications

Authors: Marek Kowalik, Ellen Michael, Peter Pogány, Phalgun Lolur

arXiv ID: 2504.11399 | Date: 2025-04-15

Abstract: Quantum computing holds promise for revolutionizing computational chemistry simulations, particularly in drug discovery. However, current quantum hardware is limited by noise and scale, necessitating bridging technologies. This study provides an initial evaluation of tensor network quantum emulators, narrowed to matrix product state-based emulators, for Hamiltonian simulation of pharmaceutical molecules, with a focus on predicting the reactivity of targeted covalent drugs. We assess runtime scaling, accuracy, and resource requirements across various active space sizes, comparing performance to traditional state vector simulation methods. Our results reveal that, for accurate estimation of the expectation value trajectory of a key measurement operator - used as a quantum-derived feature for reactivity prediction - the required bond dimension in matrix product state tensor networks grows rapidly with system size, effectively negating runtime advantages for larger, chemically relevant molecules. This study highlights the fundamental challenges in classically simulating complex quantum chemistry systems and contributes to the support of the irreplaceability premise of quantum computers to efficiently handle strongly entangled systems. Such robustness of fault-tolerant quantum computers leads to practical advantages in drug discovery applications.

Property Inheritance for Subtensors in Tensor Train Decompositions

Authors: HanQin Cai, Longxiu Huang

arXiv ID: 2504.11396 | Date: 2025-04-15

Abstract: Tensor dimensionality reduction is one of the fundamental tools for modern data science. To address the high computational overhead, fiber-wise sampled subtensors that preserve the original tensor rank are often used in designing efficient and scalable tensor dimensionality reduction. However, the theory of property inheritance for subtensors is still underdevelopment, that is, how the essential properties of the original tensor will be passed to its subtensors. This paper theoretically studies the property inheritance of the two key tensor properties, namely incoherence and condition number, under the tensor train setting. We also show how tensor train rank is preserved through fiber-wise sampling. The key parameters introduced in theorems are numerically evaluated under various settings. The results show that the properties of interest can be well preserved to the subtensors formed via fiber-wise sampling. Overall, this paper provides several handy analytic tools for developing efficient tensor analysis methods.

A Quantum-Inspired Algorithm for Wave Simulation Using Tensor Networks

Authors: Kevin Lively, Vittorio Pagni, Gonzalo Camacho

arXiv ID: 2504.11181 | Date: 2025-04-15

Abstract: We present an efficient classical algorithm based on the construction of a unitary quantum circuit for simulating the Isotropic Wave Equation (IWE) in one, two, or three dimensions. Using an analogy with the massless Dirac equation, second order time and space derivatives in the IWE are reduced to first order, resulting in a Schrödinger equation of motion. Exact diagonalization of the unitary circuit in combination with Tensor Networks allows simulation of the wave equation with a resolution of 101310^{13} grid points on a laptop. A method for encoding arbitrary analytical functions into diagonal Matrix Product Operators is employed to prepare and evolve a Matrix Product State (MPS) encoding the solution. Since the method relies on the Quantum Fourier Transform, which has been shown to generate small entanglement when applied to arbitrary MPSs, simulating the evolution of initial conditions with sufficiently low bond dimensions to high accuracy becomes highly efficient, up to the cost of Trotterized propagation and sampling of the wavefunction. We conclude by discussing possible extensions of the approach for carrying out Tensor Network simulations of other partial differential equations such as Maxwell's equations.

Nonstabilizerness in open XXZ spin chains: Universal scaling and dynamics

Authors: Doru Sticlet, Balázs Dóra, Dominik Szombathy, Gergely Zaránd, Cătălin Paşcu Moca

arXiv ID: 2504.11139 | Date: 2025-04-15

Abstract: Magic, or nonstabilizerness, is a crucial quantum resource, yet its dynamics in open quantum systems remain largely unexplored. We investigate magic in the open XXZ spin chain under either boundary gain and loss, or bulk dephasing using the stabilizer Rényi entropy M2M_2. To enable scalable simulations of large systems, we develop a novel, highly efficient algorithm for computing M2M_2 within the matrix product states formalism while maintaining constant bond dimension--an advancement over existing methods. For boundary driving, we uncover universal scaling laws, M2(t)t1/zM_2(t) \sim t^{1/z}, linked to the dynamical exponent zz for several distinct universality classes. We also disentangle classical and quantum contributions to magic by introducing a mean-field approximation for magic, thus emphasizing the prominent role of quantum critical fluctuations in nonstabilizerness. For bulk dephasing, dissipation can transiently enhance magic before suppressing it, and drive it to a nontrivial steady-state value. These findings position magic as a powerful diagnostic tool for probing universality and dynamics in open quantum systems.

Symmetry-protected topological order identified via Gutzwiller-guided density-matrix-renormalization-group: SO(n)\mathrm{SO}(n) spin chains

Authors: Pei-Yuan Cai, Hui-Ke Jin, Yi Zhou

arXiv ID: 2504.10919 | Date: 2025-04-15

Abstract: We present a comprehensive study of topological phases in the SO(nn) spin chains using a combination of analytical parton construction and numerical techniques. For even n=2ln=2l, we identify a novel SPT2^2 phase characterized by two distinct topological sectors, exhibiting exact degeneracy at the matrix product state (MPS) exactly solvable point. Through Gutzwiller-projected mean-field theory and density matrix renormalization group (DMRG) calculations, we demonstrate that these sectors remain topologically degenerate in close chains throughout the SPT2^2 phase, with energy gaps decaying exponentially with system size. For odd n=2l+1n=2l+1, we show that the ground state remains unique in close chains. We precisely characterize critical states using entanglement entropy scaling, confirming the central charges predicted by conformal field theories. Our results reveal fundamental differences between even and odd nn cases, provide numerical verification of topological protection, and establish reliable methods for studying high-symmetry quantum systems. The Gutzwiller-guided DMRG is demonstrated to be notably efficient in targeting specific topological sectors.

Algorithmic Advances Towards a Realizable Quantum Lattice Boltzmann Method

Authors: Apurva Tiwari, Jason Iaconis, Jezer Jojo, Sayonee Ray, Martin Roetteler, Chris Hill, Jay Pathak

arXiv ID: 2504.10870 | Date: 2025-04-15

Abstract: The Quantum Lattice Boltzmann Method (QLBM) is one of the most promising approaches for realizing the potential of quantum computing in simulating computational fluid dynamics. Many recent works mostly focus on classical simulation, and rely on full state tomography. Several key algorithmic issues like observable readout, data encoding, and impractical circuit depth remain unsolved. As a result, these are not directly realizable on any quantum hardware. We present a series of novel algorithmic advances which allow us to implement the QLBM algorithm, for the first time, on a quantum computer. Hardware results for the time evolution of a 2D Gaussian initial density distribution subject to a uniform advection-diffusion field are presented. Furthermore, 3D simulation results are presented for particular non-uniform advection fields, devised so as to avoid the problem of diminishing probability of success due to repeated post-selection operations required for multiple timesteps. We demonstrate the evolution of an initial quantum state governed by the advection-diffusion equation, accounting for the iterative nature of the explicit QLBM algorithm. A tensor network encoding scheme is used to represent the initial condition supplied to the advection-diffusion equation, significantly reducing the two-qubit gate count affording a shorter circuit depth. Further reductions are made in the collision and streaming operators. Collectively, these advances give a path to realizing more practical, 2D and 3D QLBM applications with non-trivial velocity fields on quantum hardware.

Heat operator approach to quantum stochastic thermodynamics in the strong-coupling regime

Authors: Sheikh Parvez Mandal, Mahasweta Pandit, Khalak Mahadeviya, Mark T. Mitchison, Javier Prior

arXiv ID: 2504.10631 | Date: 2025-04-14

Abstract: Heat exchanged between an open quantum system and its environment exhibits fluctuations that carry crucial signatures of the underlying dynamics. Within the well-established two-point measurement scheme, we identify a 'heat operator,' whose moments with respect to the vacuum state of a thermofield-doubled Hilbert space correspond to the stochastic moments of the heat exchanged with a bath. This recasts heat statistics as a unitary time evolution problem, which we solve by combining chain-mapped reservoirs with tensor network propagation. In a multi-bath setup all total and bath-resolved heat moments then follow from a single pure state evolution. We employ this approach to compute transient and steady state heat fluctuations in Ohmic spin-boson models in and out of equilibrium, accessing the challenging low temperature and long memory time regimes of the environment. In the nonequilibrium case, we show a crossover in the Fano factor from super-Poissonian to nearly Poissonian statistics under strong coupling asymmetry, corresponding to thermal rectification behavior. The method applies to noninteracting (bosonic or fermionic) nonequilibrium environments with arbitrary spectral densities, offering a powerful, non-perturbative framework for understanding heat transfer in open quantum systems.

Universal fault-tolerant logic with heterogeneous holographic codes

Authors: Matthew Steinberg, Junyu Fan, Jens Eisert, Sebastian Feld, Alexander Jahn, Chunjun Cao

arXiv ID: 2504.10386 | Date: 2025-04-14

Abstract: The study of holographic bulk-boundary dualities has led to the construction of novel quantum error correcting codes. Although these codes have shed new light on conceptual aspects of these dualities, they have widely been believed to lack a crucial feature of practical quantum error correction: The ability to support universal fault-tolerant quantum logic. In this work, we introduce a new class of holographic codes that realize this feature. These heterogeneous holographic codes are constructed by combining two seed codes in a tensor network on an alternating hyperbolic tiling. We show how this construction generalizes previous strategies for fault tolerance in tree-type concatenated codes, allowing one to implement non-Clifford gates fault-tolerantly on the holographic boundary. We also demonstrate that these codes allow for high erasure thresholds under a suitable heterogeneous combination of specific seed codes. Compared to previous concatenated codes, heterogeneous holographic codes achieve large overhead savings in physical qubits, e.g., a 21.8%21.8\% reduction for a two-layer Steane/quantum Reed-Muller combination. Unlike standard concatenated codes, we establish that the new codes can encode more than a single logical qubit per code block by applying ``black hole'' deformations with tunable rate and distance, while possessing fully addressable, universal fault-tolerant gate sets. Therefore, our work strengthens the case for the utility of holographic quantum codes for practical quantum computing.

Cross-talk in superconducting qubit lattices with tunable couplers -- comparing transmon and fluxonium architectures

Authors: F. Lange, L. Heunisch, H. Fehske, D. P. DiVincenzo, M. J. Hartmann

arXiv ID: 2504.10298 | Date: 2025-04-14

Abstract: Cross-talk between qubits is one of the main challenges for scaling superconducting quantum processors. Here, we use the density-matrix renormalization-group to numerically analyze lattices of superconducting qubits from a perspective of many-body localization. Specifically, we compare different architectures that include tunable couplers designed to decouple qubits in the idle state, and calculate the residual ZZ interactions as well as the inverse participation ratio in the computational basis states. For transmon qubits outside of the straddling regime, the results confirm that tunable C-shunt flux couplers are significantly more efficient in mitigating the ZZ interactions than tunable transmons. A recently proposed fluxonium architecture with tunable transmon couplers is demonstrated to also maintain its strong suppression of the ZZ interactions in larger systems, while having a higher inverse participation ratio in the computational basis states than lattices of transmon qubits. Our results thus suggest that fluxonium architectures may feature lower cross talk than transmon lattices when designed to achieve similar gate speeds and fidelities.

An Exact Link between Nonlocal Nonstabilizerness and Operator Entanglement

Authors: Faidon Andreadakis, Paolo Zanardi

arXiv ID: 2504.09360 | Date: 2025-04-12

Abstract: Nonstabilizerness is a quantum property of states associated with the non-Clifford resources required for their preparation. As a resource, nonstabilizerness complements entanglement, and the interplay between these two concepts has garnered significant attention in recent years. In this work, we establish an exact correspondence between the generation of nonlocal nonstabilizerness and operator entanglement under unitary evolutions. Nonlocal nonstabilizerness refers to nonstabilizerness that cannot be erased via local operations, while operator entanglement generalizes entanglement to operator space, characterizing the complexity of operators across a bipartition. Specifically, we prove that a unitary map generates nonlocal nonstabilizerness if and only if it generates operator entanglement on Pauli strings. Guided by this result, we introduce an average measure of a unitary's Pauli-entangling power, serving as a proxy for nonlocal nonstabilizerness generation. We derive analytical formulas for this measure and examine its properties, including its typical value and upper bounds in terms of the nonstabilizerness properties of the evolution.

Adiabatic Encoding of Pre-trained MPS Classifiers into Quantum Circuits

Authors: Keisuke Murota

arXiv ID: 2504.09250 | Date: 2025-04-12

Abstract: Although Quantum Neural Networks (QNNs) offer powerful methods for classification tasks, the training of QNNs faces two major training obstacles: barren plateaus and local minima. A promising solution is to first train a tensor-network (TN) model classically and then embed it into a QNN.\ However, embedding TN-classifiers into quantum circuits generally requires postselection whose success probability may decay exponentially with the system size. We propose an \emph{adiabatic encoding} framework that encodes pre-trained MPS-classifiers into quantum MPS (qMPS) circuits with postselection, and gradually removes the postselection while retaining performance. We prove that training qMPS-classifiers from scratch on a certain artificial dataset is exponentially hard due to barren plateaus, but our adiabatic encoding circumvents this issue. Additional numerical experiments on binary MNIST also confirm its robustness.

SW-TNC : Reaching the Most Complex Random Quantum Circuit via Tensor Network Contraction

Authors: Yaojian Chen, Zhaoqi Sun, Chengyu Qiu, Zegang Li, Yanfei Liu, Lin Gan, Xiaohui Duan, Guangwen Yang

arXiv ID: 2504.09186 | Date: 2025-04-12

Abstract: Classical simulation is essential in quantum algorithm development and quantum device verification. With the increasing complexity and diversity of quantum circuit structures, existing classical simulation algorithms need to be improved and extended. In this work, we propose novel strategies for tensor network contraction based simulator on Sunway architecture. Our approach addresses three main aspects: complexity, computational paradigms and fine-grained optimization. Data reuse schemes are designed to reduce floating-point operations, and memory organization techniques are employed to eliminate slicing overhead while maintaining parallelism. Step fusion strategy is extended by multi-core cooperation to improve the data locality and computation intensity. Fine-grained optimizations, such as in-kernel vectorized permutations, and split-K operators, are developed as well to address the challenges in new hotspot distribution and topological structure. These innovations can accelerate the simulation of the Zuchongzhi-60-24 by more than 10 times, using more than 1024 Sunway nodes (399,360 cores). Our work demonstrates the potential for enabling efficient classical simulation of increasingly complex quantum circuits.

Spectral signatures of residual electron pairing in the extended-Hubbard-Su-Schrieffer-Heeger model

Authors: Debshikha Banerjee, Alberto Nocera, George A. Sawatzky, Mona Berciu, Steven Johnston

arXiv ID: 2504.09020 | Date: 2025-04-12

Abstract: We study the electron addition spectrum of the one-dimensional extended Hubbard-Su-Schrieffer-Heeger (HSSH) model in the dilute limit using the density matrix renormalization group method. In addition to the expected renormalization to the band structure, we find that the electron-phonon (e-ph) interaction produces an anomalous spectral feature when electrons are added in the singlet channel but which is absent in the triplet channel. By comparing these results with those obtained from perturbation theory in the antiadiabatic limit, we demonstrate that this anomalous feature is a remnant of the strong electron-electron interaction mediated by the SSH coupling previously derived in the two-particle limit. By studying the evolution of this feature as a function of doping, we track the fate of this attraction to higher carrier concentrations and provide predictions for the spectral features to help guide future searches for strong e-ph mediated pairing.

Inhomogeneous entanglement structure in monoaxial chiral ferromagnetic quantum spin chain

Authors: Kentaro Nishimura, Ryosuke Yoshii

arXiv ID: 2504.08273 | Date: 2025-04-11

Abstract: Chiral magnets, characterized by inhomogeneous magnetic moment arrangements, have attracted significant attention recently due to their topological orders, such as magnetic skyrmion lattices and chiral soliton lattices. In this work, we investigate the entanglement entropy of \textit{quantum} chiral magnets and demonstrate that it reflects the inhomogeneous nature of the ground state. We perform numerical simulations of a one-dimensional monoaxial chiral ferromagnetic chain with Zeeman term using the density matrix renormalization group method. Our results show that the entanglement entropy exhibits oscillatory behavior, which can be tuned by varying the external magnetic field. Analysis of the local magnetization and spin chirality further confirms that these oscillations correspond to solitonic structures. Moreover, our findings suggest that the entanglement entropy can serve as a probe for detecting the vacuum structure, providing new insights into quantum correlations.

Fractional Chern Insulator and Quantum Anomalous Hall Crystal in Twisted MoTe2_2

Authors: Jialin Chen, Qiaoyi Li, Xiaoyu Wang, Wei Li

arXiv ID: 2504.07932 | Date: 2025-04-10

Abstract: Recent experimental advances have uncovered fractional Chern insulators in twisted MoTe2_2 (tMoTe2_2) systems, posing significant theoretical challenges in understanding the interaction effects and correlated topological phases. Here, we construct a realistic moiré lattice model tailored for tMoTe2_2 and conduct investigations using state-of-the-art tensor-network methods. Our ground-state calculations reveal a rich array of interaction- and filling-dependent phases, including the FCI, Chern insulator, and generalized Wigner crystal, etc., explaining recent experimental observations. Moreover, we reveal quantum anomalous Hall crystals exhibiting integer Hall conductivity at fractional moiré unit cell fillings, which opens new avenues for experimental exploration in tMoTe2_2. In the FCI phase, dynamical simulations reveal a single-particle continuum with a finite charge gap, indicating the presence of fractional charge excitations. Moreover, our finite-temperature calculations determine the characteristic temperatures for charge activation and ferromagnetic (FM) transitions, consistent with experiments. We find that the charge gap is significantly larger than the energy scales of both thermal activation and FM transitions, explaining recent experimental observations. Overall, by integrating ground-state, finite-temperature, and dynamical tensor-network calculations on the real-space model, we establish a theoretical framework for understanding and exploring correlated topological phases in tMoTe2_2 and related systems.

Renormalization group-like flows in randomly connected tensor networks

Authors: Naoki Sasakura

arXiv ID: 2504.07587 | Date: 2025-04-10

Abstract: Randomly connected tensor networks (RCTN) are the dynamical systems defined by summing over all the possible networks of tensors. Because of the absence of fixed lattice structure, RCTN is not expected to have renormalization procedures. In this paper, however, we consider RCTN with a real tensor, and it is proven that a Hamiltonian vector flow of a tensor model in the canonical formalism with a positive cosmological constant has the properties which a renormalization group (RG) flow of RCTN would have: The flow has fixed points on phase transition surfaces; every flow line is asymptotically terminated by fixed points at both ends, where an upstream fixed point has higher criticality than a downstream one; the flow goes along phase transition surfaces; there exists a function which monotonically decreases along the flow, analogously to the aa- and cc-functions of RG. A complete classification of fixed points is given. Although there are no cyclic flows in the strict sense, these exist, if infinitesimal jumps are allowed near fixed points.

Parton Distribution Functions in the Schwinger model from Tensor Network States

Authors: Mari Carmen Bañuls, Krzysztof Cichy, C. -J. David Lin, Manuel Schneider

arXiv ID: 2504.07508 | Date: 2025-04-10

Abstract: Parton distribution functions (PDFs) describe the inner, non-perturbative structure of hadrons. Their computation involves matrix elements with a Wilson line along a direction on the light cone, posing significant challenges in Euclidean lattice calculations, where the time direction is not directly accessible. We propose implementing the light-front Wilson line within the Hamiltonian formalism using tensor network techniques. The approach is demonstrated in the massive Schwinger model (quantum electrodynamics in 1+1 dimensions), a toy model that shares key features with quantum chromodynamics. We present accurate continuum results for the fermion PDF of the vector meson at varying fermion masses, obtained from first principle calculations directly in Minkowski space. Our strategy also provides a useful path for quantum simulations and quantum computing.

Quantifying the Phase Diagram and Hamiltonian of S=1/2S=1/2 Kagome Antiferromagnets: Bridging Theory and Experiment

Authors: Shengtao Jiang, Arthur C. Campello, Wei He, Jiajia Wen, Daniel M. Pajerowski, Young S. Lee, Hong-Chen Jiang

arXiv ID: 2504.07387 | Date: 2025-04-10

Abstract: Spin-1/21/2 kagome antiferromagnets are leading candidates for realizing quantum spin liquid (QSL) ground states. While QSL ground states are predicted for the pure Heisenberg model, understanding the robustness of the QSL to additional interactions that may be present in real materials is a forefront question in the field. Here we employ large-scale density-matrix renormalization group simulations to investigate the effects of next-nearest neighbor exchange couplings J2J_2 and Dzyaloshinskii-Moriya interactions DD, which are relevant to understanding the prototypical kagome materials herbertsmithite and Zn-barlowite. By utilizing clusters as large as XC12 and extrapolating the results to the thermodynamic limit, we precisely delineate the scope of the QSL phase, which remains robust across an expanded parameter range of J2J_2 and DD. Direct comparison of the simulated static and dynamic spin structure factors with inelastic neutron scattering reveals the parameter space of the Hamiltonians for herbertsmithite and Zn-barlowite, and, importantly, provides compelling evidence that both materials exist within the QSL phase. These results establish a powerful convergence of theory and experiment in this most elusive state of matter.

Simulating quantum dynamics in two-dimensional lattices with tensor network influence functional belief propagation

Authors: Gunhee Park, Johnnie Gray, Garnet Kin-Lic Chan

arXiv ID: 2504.07344 | Date: 2025-04-10

Abstract: Describing nonequilibrium quantum dynamics remains a significant computational challenge due to the growth of spatial entanglement. The tensor network influence functional (TN-IF) approach mitigates this problem for computing the time evolution of local observables by encoding the subsystem's influence functional path integral as a matrix product state (MPS), thereby shifting the resource governing computational cost from spatial entanglement to temporal entanglement. We extend the applicability of the TN-IF method to two-dimensional lattices by demonstrating its construction on tree lattices and proposing a belief propagation (BP) algorithm for the TN-IF, termed influence functional BP (IF-BP), to simulate local observable dynamics on arbitrary graphs. Even though the BP algorithm introduces uncontrolled approximation errors on arbitrary graphs, it provides an accurate description for locally tree-like lattices. Numerical simulations of the kicked Ising model on a heavy-hex lattice, motivated by a recent quantum experiment, highlight the effectiveness of the IF-BP method, which demonstrates superior performance in capturing long-time dynamics where traditional tensor network state-based methods struggle. Our results further reveal that the temporal entanglement entropy (TEE) only grows logarithmically with time for this model, resulting in a polynomial computational cost for the whole method. We further construct a cluster expansion of IF-BP to introduce loop correlations beyond the BP approximation, providing a systematic correction to the IF-BP estimate. We demonstrate the power of the cluster expansion of the IF-BP in simulating the quantum quench dynamics of the 2D transverse field Ising model, obtaining numerical results that improve on the state-of-the-art.

Simulating quantum dynamics in two-dimensional lattices with tensor network influence functional belief propagation

Authors: Gunhee Park, Johnnie Gray, Garnet Kin-Lic Chan

arXiv ID: 2504.07344 | Date: 2025-04-10

Abstract: Describing nonequilibrium quantum dynamics remains a significant computational challenge due to the growth of spatial entanglement. The tensor network influence functional (TN-IF) approach mitigates this problem for computing the time evolution of local observables by encoding the subsystem's influence functional path integral as a matrix product state (MPS), thereby shifting the resource governing computational cost from spatial entanglement to temporal entanglement. We extend the applicability of the TN-IF method to two-dimensional lattices by demonstrating its construction on tree lattices and proposing a belief propagation (BP) algorithm for the TN-IF, termed influence functional BP (IF-BP), to simulate local observable dynamics on arbitrary graphs. Even though the BP algorithm introduces uncontrolled approximation errors on arbitrary graphs, it provides an accurate description for locally tree-like lattices. Numerical simulations of the kicked Ising model on a heavy-hex lattice, motivated by a recent quantum experiment, highlight the effectiveness of the IF-BP method, which demonstrates superior performance in capturing long-time dynamics where traditional tensor network state-based methods struggle. Our results further reveal that the temporal entanglement entropy (TEE) only grows logarithmically with time for this model, resulting in a polynomial computational cost for the whole method. We further construct a cluster expansion of IF-BP to introduce loop correlations beyond the BP approximation, providing a systematic correction to the IF-BP estimate. We demonstrate the power of the cluster expansion of the IF-BP in simulating the quantum quench dynamics of the 2D transverse field Ising model, obtaining numerical results that improve on the state-of-the-art.

Efficient mutual magic and magic capacity with matrix product states

Authors: Poetri Sonya Tarabunga, Tobias Haug

arXiv ID: 2504.07230 | Date: 2025-04-09

Abstract: Stabilizer Rényi entropies (SREs) probe the non-stabilizerness (or magic) of many-body systems and quantum computers. Here, we introduce the mutual von-Neumann SRE and magic capacity, which can be efficiently computed in time O(Nχ3)O(Nχ^3) for matrix product states (MPSs) of bond dimension χχ. We find that mutual SRE characterizes the critical point of ground states of the transverse-field Ising model, independently of the chosen local basis. Then, we relate the magic capacity to the anti-flatness of the Pauli spectrum, which quantifies the complexity of computing SREs. The magic capacity characterizes transitions in the ground state of the Heisenberg and Ising model, randomness of Clifford+T circuits, and distinguishes typical and atypical states. Finally, we make progress on numerical techniques: we design two improved Monte-Carlo algorithms to compute the mutual 22-SRE, overcoming limitations of previous approaches based on local update. We also give improved statevector simulation methods for Bell sampling and SREs with O(8N/2)O(8^{N/2}) time and O(2N)O(2^N) memory, which we demonstrate for 2424 qubits. Our work uncovers improved approaches to study the complexity of quantum many-body systems.

Plastic tensor networks for interpretable generative modeling

Authors: Katsuya O. Akamatsu, Kenji Harada, Tsuyoshi Okubo, Naoki Kawashima

arXiv ID: 2504.06722 | Date: 2025-04-09

Abstract: A structural optimization scheme for a single-layer nonnegative adaptive tensor tree (NATT) that models a target probability distribution is proposed as an alternative paradigm for generative modeling. The NATT scheme, by construction, automatically searches for a tree structure that best fits a given discrete dataset whose features serve as inputs, and has the advantage that it is interpretable as a probabilistic graphical model. We consider the NATT scheme and a recently proposed Born machine adaptive tensor tree (BMATT) optimization scheme and demonstrate their effectiveness on a variety of generative modeling tasks where the objective is to infer the hidden structure of a provided dataset. Our results show that in terms of minimizing the negative log-likelihood, the single-layer scheme has model performance comparable to the Born machine scheme, though not better. The tasks include deducing the structure of binary bitwise operations, learning the internal structure of random Bayesian networks given only visible sites, and a real-world example related to hierarchical clustering where a cladogram is constructed from mitochondrial DNA sequences. In doing so, we also show the importance of the choice of network topology and the versatility of a least-mutual information criterion in selecting a candidate structure for a tensor tree, as well as discuss aspects of these tensor tree generative models including their information content and interpretability.

Experimental Implementation of a Qubit-Efficient Variational Quantum Eigensolver with Analog Error Mitigation on a Superconducting Quantum Processor

Authors: Yuwei Ma, Weiting Wang, Xianghao Mu, Weizhou Cai, Ziyue Hua, Xiaoxuan Pan, Dong-Ling Deng, Rebing Wu, Chang-Ling Zou, Lei Wang, Luyan Sun

arXiv ID: 2504.06554 | Date: 2025-04-09

Abstract: We experimentally demonstrate a qubit-efficient variational quantum eigensolver (VQE) algorithm using a superconducting quantum processor, employing minimal quantum resources with only a transmon qubit coupled to a high-coherence photonic qubit. By leveraging matrix product states to compress the quantum state representation, we simulate an N + 1-spin circular Ising model with a transverse field. Furthermore, we develop an analog error mitigation approach through zero-noise extrapolation by introducing a precise noise injection technique for the transmon qubit. As a validation, we apply our error-mitigated qubit-efficient VQE in determining the ground state energies of a 4-spin Ising model. Our results demonstrate the feasibility of performing quantum algorithms with minimal quantum resources while effectively mitigating the impact of noise, offering a promising pathway to bridge the gap between theoretical advances and practical implementations on current noisy intermediate-scale quantum devices.

Identifying Universal Spin Excitations in Spin-1/2 Kagome Quantum Spin Liquid Materials

Authors: Aaron T. Breidenbach, Arthur C. Campello, Jiajia Wen, Hong-Chen Jiang, Daniel M. Pajerowski, Rebecca W. Smaha, Young S. Lee

arXiv ID: 2504.06491 | Date: 2025-04-08

Abstract: A quantum spin liquid (QSL) is an exotic quantum state of matter characterized by fluctuating spins which may exhibit long-range entanglement. Among the possible host candidates for a QSL ground state, the SS=1/2 kagome lattice antiferromagnet is particularly promising. Using high resolution inelastic neutron scattering measurements on Zn-barlowite (Znx_\mathrm{x}Cu4x_\mathrm{4-x}(OD)6_\mathrm{6}FBr, x0.80x\simeq 0.80), we measure a spin excitation spectrum consistent with a QSL ground state. Continuum scattering above \sim1 meV matches that of herbertsmithite (Znx_\mathrm{x}Cu4x_\mathrm{4-x}(OD)6_6Cl2_2, x0.85x\simeq 0.85), another prominent kagome QSL material, indicating universal spinon excitations. A detailed analysis of the spin-spin correlations, compared with density matrix renormalization group calculations, further indicate a QSL ground state for the physically relevant Hamiltonian parameters. The measured spectra in Zn-barlowite are consistent with gapped behavior with a gap size Δ=1.1(2)Δ= 1.1(2) meV. Comparison with a simple pair correlation model allows us to clearly distinguish intrinsic kagome correlations from impurity-induced correlations. Our results clarify the behavior that is universal within this important family of QSL candidate materials.

Successive randomized compression: A randomized algorithm for the compressed MPO-MPS product

Authors: Chris Camaño, Ethan N. Epperly, Joel A. Tropp

arXiv ID: 2504.06475 | Date: 2025-04-08

Abstract: Tensor networks like matrix product states (MPSs) and matrix product operators (MPOs) are powerful tools for representing exponentially large states and operators, with applications in quantum many-body physics, machine learning, numerical analysis, and other areas. In these applications, computing a compressed representation of the MPO--MPS product is a fundamental computational primitive. For this operation, this paper introduces a new single-pass, randomized algorithm, called successive randomized compression (SRC), that improves on existing approaches in speed or in accuracy. The performance of the new algorithm is evaluated on synthetic problems and unitary time evolution problems for quantum spin systems.

FETTA: Flexible and Efficient Hardware Accelerator for Tensorized Neural Network Training

Authors: Jinming Lu, Jiayi Tian, Hai Li, Ian Young, Zheng Zhang

arXiv ID: 2504.06474 | Date: 2025-04-08

Abstract: The increasing demand for on-device training of deep neural networks (DNNs) aims to leverage personal data for high-performance applications while addressing privacy concerns and reducing communication latency. However, resource-constrained platforms face significant challenges due to the intensive computational and memory demands of DNN training. Tensor decomposition emerges as a promising approach to compress model size without sacrificing accuracy. Nevertheless, training tensorized neural networks (TNNs) incurs non-trivial overhead and severe performance degradation on conventional accelerators due to complex tensor shaping requirements. To address these challenges, we propose FETTA, an algorithm and hardware co-optimization framework for efficient TNN training. On the algorithm side, we develop a contraction sequence search engine (CSSE) to identify the optimal contraction sequence with the minimal computational overhead. On the hardware side, FETTA features a flexible and efficient architecture equipped with a reconfigurable contraction engine (CE) array to support diverse dataflows. Furthermore, butterfly-based distribution and reduction networks are implemented to perform flexible tensor shaping operations during computation. Evaluation results demonstrate that FETTA achieves reductions of 20.5x/100.9x, 567.5x/45.03x, and 11609.7x/4544.8x in terms of processing latency, energy, and energy-delay product (EDP) over GPU and TPU, respectively. Moreover, working on the tensorized training, FETTA outperforms prior accelerators with a speedup of 3.87~14.63x, and an energy efficiency improvement of 1.41~2.73x on average.

Comparative Analysis of Classical and Quantum-Inspired Solvers: A Preliminary Study on the Weighted Max-Cut Problem

Authors: Aitor Morais, Eneko Osaba, Iker Pastor, Izaskun Oregui

arXiv ID: 2504.05989 | Date: 2025-04-08

Abstract: Combinatorial optimization is essential across numerous disciplines. Traditional metaheuristics excel at exploring complex solution spaces efficiently, yet they often struggle with scalability. Deep learning has become a viable alternative for quickly generating high-quality solutions, particularly when metaheuristics underperform. In recent years, quantum-inspired approaches such as tensor networks have shown promise in addressing these challenges. Despite these advancements, a thorough comparison of the different paradigms is missing. This study evaluates eight algorithms on Weighted Max-Cut graphs ranging from 10 to 250 nodes. Specifically, we compare a Genetic Algorithm representing metaheuristics, a Graph Neural Network for deep learning, and the Density Matrix Renormalization Group as a tensor network approach. Our analysis focuses on solution quality and computational efficiency (i.e., time and memory usage). Numerical results show that the Genetic Algorithm achieves near-optimal results for small graphs, although its computation time grows significantly with problem size. The Graph Neural Network offers a balanced solution for medium-sized instances with low memory demands and rapid inference, yet it exhibits more significant variability on larger graphs. Meanwhile, the Tensor Network approach consistently yields high approximation ratios and efficient execution on larger graphs, albeit with increased memory consumption.

Functional matrix product state simulation of continuous variable quantum circuits

Authors: Andreas Bock Michelsen, Frederik K. Marqversen, Michael Kastoryano

arXiv ID: 2504.05860 | Date: 2025-04-08

Abstract: We introduce a functional matrix product state (FMPS) based method for simulating the real-space representation of continuous-variable (CV) quantum computation. This approach efficiently simulates non-Gaussian CV systems by leveraging their functional form. By addressing scaling bottlenecks, FMPS enables more efficient simulation of shallow, multi-mode CV quantum circuits with non-Gaussian input states. The method is validated by simulating random shallow and cascaded circuits with highly non-Gaussian input states, showing superior performance compared to existing techniques, also in the presence of loss.

Benchmarking vibrational spectra: 5000 accurate eigenstates of acetonitrile using tree tensor network states

Authors: Henrik R. Larsson

arXiv ID: 2504.05382 | Date: 2025-04-07

Abstract: Accurate vibrational spectra are essential for understanding how molecules behave, yet their computation remains challenging and benchmark data to reliably compare different methods are sparse. Here, we present high-accuracy eigenstate computations for the six-atom, 12-dimensional acetonitrile molecule, a prototypical, strongly coupled, anharmonic system. Using a density matrix renormalization group (DMRG) algorithm with a tree-tensor-network-state (TTNS) ansatz, a refinement using TTNSs as basis set, and reliable procedures to estimate energy errors, we compute up to 5,000 vibrational states with error estimates below 0.0007 cm1\mathrm{cm}^{-1}. Our analysis reveals that previous works underestimated the energy error by up to two orders of magnitude. Our data serve as a benchmark for future vibrational spectroscopy methods and our new method offers a path toward similarly precise computations of large, complex molecular systems.

Probabilistic imaginary-time evolution in state-vector-based and shot-based simulations and on quantum devices

Authors: Satoshi Ejima, Kazuhiro Seki, Benedikt Fauseweh, Seiji Yunoki

arXiv ID: 2504.04958 | Date: 2025-04-07

Abstract: Imaginary-time evolution, an important technique in tensor network and quantum Monte Carlo algorithms on classical computers, has recently been adapted to quantum computing. In this study, we focus on probabilistic imaginary-time evolution (PITE) algorithm and derive its formulation in the context of state-vector-based simulations, where quantum state vectors are directly used to compute observables without statistical errors. We compare the results with those of shot-based simulations, which estimate observables through repeated projective measurements. Applying the PITE algorithm to the Heisenberg chain, we investigate optimal initial conditions for convergence. We further demonstrate the method on the transverse-field Ising model using a state-of-the-art trapped-ion quantum device. Finally, we explore the potential of error mitigation in this framework, highlighting practical considerations for near-term digital quantum simulations.

Scalable projected entangled-pair state representation of random quantum circuit states

Authors: Sung-Bin B. Lee, Hee Ryang Choi, Daniel Donghyon Ohm, Seung-Sup B. Lee

arXiv ID: 2504.04769 | Date: 2025-04-07

Abstract: Classical simulation of a programmable quantum processor is crucial in identifying the threshold of a quantum advantage. We demonstrate the simple update of projected entangled-pair states (PEPSs) in the Vidal gauge that represent random quantum circuit states, which center around recent quantum advantage claims. Applied to square lattices of qubits akin to state-of-the-art superconducting processors, the PEPS representation is exact for circuit depths less than Dtr\mathcal{D}_\mathrm{tr} = βlog2χβ\log_2χ, where χχ is the maximum bond dimension and 2β42 \lesssim β\lesssim 4 depends on the choice of two-qubit gates, independent of the qubit number nn. We find the universal scaling behaviors of the state fidelity by treating large-scale circuits of n104n \leq 10^{4}, using χ128χ\leq 128 on a conventional CPU. Our method has a polynomial scaling of computational costs with nn for circuit depth D=O(logn)\mathcal{D}=O(\log n) and is more advantageous than matrix product state approaches if nn is large. This work underscores PEPSs as a scalable tool for benchmarking quantum algorithms with future potential for sampling applications using advanced contraction techniques.

Symmetrizing the Constraints -- Density Matrix Renormalization Group for Constrained Lattice Models

Authors: Ting-Tung Wang, Xiaoxue Ran, Zi Yang Meng

arXiv ID: 2504.04035 | Date: 2025-04-05

Abstract: We develop a density matrix renormalization group (DMRG) algorithm for constrained quantum lattice models that successfully {\it{implements the local constraints as symmetries in the contraction of the matrix product states and matrix product operators}}. Such an implementation allows us to investigate a quantum dimer model in DMRG for any lattice geometry wrapped around a cylinder with substantial circumference. We have thence computed the ground state phase diagram of the quantum dimer model on triangular lattice, with the symmetry-breaking characteristics of the columnar solid phase and 12×12\sqrt{12}\times\sqrt{12} valence bond solid phase fully captured, as well as the topological entanglement entropy of the Z2\mathbb{Z}_2 quantum spin liquid phase that extends to the RK point on non-bipartite lattice accurately revealed. Our DMRG algorithm on constrained quantum lattice models opens new opportunities for matrix and tensor-based algorithms for these systems that have immediate relevance towards the frustrated quantum magnets and synthetic quantum simulators.

Exotic Doublon-Holon Pairing State in Photodoped Mott Insulators

Authors: Ryota Ueda, Madhumita Sarkar, Zala Lenarčič, Denis Golež, Kazuhiko Kuroki, Tatsuya Kaneko

arXiv ID: 2504.03324 | Date: 2025-04-04

Abstract: We demonstrate the existence of a unique pairing state in photodoped Mott insulators on ladder geometries, characterized by quasi-long-ranged doublon-holon correlations, using the density matrix renormalization group method. This phase exhibits doublon-holon pairing correlations with opposite signs along the rung and chain directions, reminiscent of d-wave pairing in chemically doped ladder systems. By constructing the phase diagram, we reveal that the doublon-holon pairing state emerges between the spin-singlet phase and the charge-density-wave/ηη-pairing phase. Our study suggests that the interplay of charge, spin, and ηη-spin degrees of freedom can give rise to exotic quantum many-body states in photodoped Mott insulators.

Compositionality Unlocks Deep Interpretable Models

Authors: Thomas Dooms, Ward Gauderis, Geraint A. Wiggins, Jose Oramas

arXiv ID: 2504.02667 | Date: 2025-04-03

Abstract: We propose χχ-net, an intrinsically interpretable architecture combining the compositional multilinear structure of tensor networks with the expressivity and efficiency of deep neural networks. χχ-nets retain equal accuracy compared to their baseline counterparts. Our novel, efficient diagonalisation algorithm, ODT, reveals linear low-rank structure in a multilayer SVHN model. We leverage this toward formal weight-based interpretability and model compression.

Finite steady-state current defies non-Hermitian many-body localization

Authors: Pietro Brighi, Marko Ljubotina, Federico Roccati, Federico Balducci

arXiv ID: 2504.02460 | Date: 2025-04-03

Abstract: Non-Hermitian many-body localization (NH MBL) has emerged as a possible scenario for stable localization in open systems, as suggested by spectral indicators identifying a putative transition for finite system sizes. In this work, we shift the focus to dynamical probes, specifically the steady-state spin current, to investigate transport properties in a disordered, non-Hermitian XXZ spin chain. Through exact diagonalization for small systems and tensor-network methods for larger chains, we demonstrate that the steady-state current remains finite and decays exponentially with disorder strength, showing no evidence of a transition up to disorder values far beyond the previously claimed critical point. Our results reveal a stark discrepancy between spectral indicators, which suggest localization, and transport behavior, which indicates delocalization. This highlights the importance of dynamical observables in characterizing NH MBL and suggests that traditional spectral measures may not fully capture the physics of non-Hermitian systems. Additionally, we observe a non-commutativity of limits in system size and time, further complicating the interpretation of finite-size studies. These findings challenge the existence of NH MBL in the studied model and underscore the need for alternative approaches to understand localization in non-Hermitian settings.

Perturbative Variational Quantum Eigensolver based on Reduced Density Matrix Method

Authors: Yuhan Zheng, Yibin Guo, Huili Zhang, Jie Liu, Xiongzhi Zeng, Xiaoxia Cai, Zhenyu Li, Jinlong Yang

arXiv ID: 2504.02340 | Date: 2025-04-03

Abstract: Current noisy intermediate-scale quantum (NISQ) devices lack the quantum resources required for practical applications. To address this, we propose the perturbative variational quantum eigensolver (PT-VQE). In PT-VQE, VQE is used to capture key correlations within a carefully selected active space, while perturbation theory efficiently incorporates interactions in the remaining space, without requiring additional qubits or circuit depth. When the VQE-optimized state closely approximates the true ground state in the active space, excitations cannot act solely in the active space, since their contributions to perturbative correction are negligible. This reduces the highest-order required RDM from 4-RDM to 3-RDM, significantly reducing computational costs. We validate PT-VQE by calculating the ground-state potential energy surfaces (PESs) of HF\rm{HF} and N2\rm{N}_2, as well as the ground-state energy of ferrocene (Fe(C5H5)2\rm{Fe(C_5H_5)_2}). Additionally, PT-VQE is performed on a quantum computer to compute the PES of F2{\rm F}_2. The consistent results obtained from both PT-VQE with the highest 3-RDM and 4-RDM confirm the reliability of the constraint. PT-VQE significantly outperforms standard VQE, achieving chemical accuracy. This method offers a resource-efficient and practical approach for accurate quantum simulations of larger systems.

Topological Phase Transition in the Two-Leg Hubbard Model: Emergence of the Haldane Phase via Diagonal Hopping and Strong Interactions

Authors: João Pedro Gama D'Elia, Thereza Paiva

arXiv ID: 2504.02157 | Date: 2025-04-02

Abstract: We investigate the two-leg Hubbard model with diagonal hopping to explore the interplay between geometrical frustration and strong electron-electron interactions. Using the Density Matrix Renormalization Group (DMRG) method, we demonstrate the emergence of a topological Haldane phase, which results explicitly from the complementary effects of diagonal hopping-induced frustration and strong on-site Coulomb repulsion. The topological phase transition from a trivial insulator to the nontrivial Haldane phase is characterized by significant changes in magnetic properties, edge correlations, and the appearance of a nonzero string order parameter. Furthermore, we confirm the topological nature of this phase through a detailed analysis of the spin gap and entanglement spectrum, demonstrating clear signatures of symmetry-protected topological order.

Low-energy structure and topology of the two-band Hubbard-Kanamori model

Authors: Nayara G. Gusmão, Germán Blesio, Armando Aligia, Walber H. Brito, Maria C. O. Aguiar, Karen Hallberg

arXiv ID: 2504.01269 | Date: 2025-04-02

Abstract: We investigate the Mott transition in a two-band Hubbard-Kanamori model using Dynamical Mean-Field Theory (DMFT) with the Density Matrix Renormalization Group (DMRG) and the Numerical Renormalization Group (NRG) as impurity solvers. Our study focuses on the case where the intraorbital and interorbital Coulomb interactions are equal (U = U2) and the Hund's coupling is absent (J = 0). Spectral analysis confirms the absence of an orbital-selective Mott transition (OSMT), even in systems with significantly different bandwidths (t1 and t2 for the wide and narrow bands, respectively), indicating a simultaneous Mott transition in both bands. Notably, the NRG results reveal the emergence of a pseudo-gap-like feature and a central peak in the narrow band, whose characteristics depend on the hopping parameter t2. These spectral features may serve as precursors to OSMT in more realistic systems with finite Hund's coupling (J > 0). Furthermore, in the Mott insulating phase, the self-energies of both bands diverge, suggesting that the Mott transition represents a topological phase transition. Our results highlight the crucial role of accurate impurity solvers in capturing the density of states and detailed spectral structures.

Multicriticality in stochastic dynamics protected by self-duality

Authors: Konstantinos Sfairopoulos, Luke Causer, Juan P. Garrahan

arXiv ID: 2504.01258 | Date: 2025-04-02

Abstract: We study the dynamical large deviations (LD) of a class of one-dimensional kinetically constrained models whose (tilted) generators can be mapped into themselves via duality transformations. We consider four representative models in detail: the domain-wall (DW) Fredrickson-Andersen (FA), the DW East, the ZZZ-FA, and the XOR-FA models. Using numerical tensor networks, we build the LD phase diagrams of these models in terms of the softness of the constraint and the counting field conjugate to the dynamical activity. In all cases, we find distinct dynamical phases separated by phase transitions along the self-dual lines, revealing the presence of multi-critical points that delimit first-order from continuous active-inactive transitions. We discuss connections to supersymmetry and possible extensions to higher spin and space dimensions.

LimTDD: A Compact Decision Diagram Integrating Tensor and Local Invertible Map Representations

Authors: Xin Hong, Aochu Dai, Dingchao Gao, Sanjiang Li, Zhengfeng Ji, Mingsheng Ying

arXiv ID: 2504.01168 | Date: 2025-04-01

Abstract: Tensor networks serve as a powerful tool for efficiently representing and manipulating high-dimensional data in applications such as quantum physics, machine learning, and data compression. Tensor Decision Diagrams (TDDs) offer an efficient framework for tensor representation by leveraging decision diagram techniques. However, the current implementation of TDDs and other decision diagrams fail to exploit tensor isomorphisms, limiting their compression potential. This paper introduces Local Invertible Map Tensor Decision Diagrams (LimTDDs), an extension of TDDs that incorporates local invertible maps (LIMs) to achieve more compact representations. Unlike LIMDD, which uses Pauli operators for quantum states, LimTDD employs the XPXP-stabilizer group, enabling broader applicability across tensor-based tasks. We present efficient algorithms for normalization, slicing, addition, and contraction, critical for tensor network applications. Theoretical analysis demonstrates that LimTDDs achieve greater compactness than TDDs and, in best-case scenarios and for quantum state representations, offer exponential compression advantages over both TDDs and LIMDDs. Experimental results in quantum circuit tensor computation and simulation confirm LimTDD's superior efficiency. Open-source code is available at https://github.com/Veriqc/LimTDD.

Exact Diagonalization, Matrix Product States and Conformal Perturbation Theory Study of a 3D Ising Fuzzy Sphere Model

Authors: Andreas M. Läuchli, Loïc Herviou, Patrick H. Wilhelm, Slava Rychkov

arXiv ID: 2504.00842 | Date: 2025-04-01

Abstract: Numerical studies of phase transitions in statistical and quantum lattice models provide crucial insights into the corresponding Conformal Field Theories (CFTs). In higher dimensions, comparing finite-volume numerical results to infinite-volume CFT data is facilitated by choosing the sphere Sd1S^{d-1} as the spatial manifold. Recently, the fuzzy sphere regulator in Ref. [Zhu et al, Phys. Rev. X 13 021009 (2023)] has enabled such studies with exact rotational invariance, yielding impressive agreement with known 3D Ising CFT predictions, as well as new results. However, systematic improvements and a deeper understanding of finite-size corrections remain essential. In this work, we revisit the fuzzy sphere regulator, focusing on the original Ising model, with two main goals. First, we assess the robustness of this approach using Conformal Perturbation Theory (CPT), to which we provide a detailed guidebook. We demonstrate how CPT provides a unified framework for determining the critical point, the speed of light, and residual deviations from CFT predictions. Applying this framework, we study finite-size corrections and clarify the role of tuning the model in minimizing these effects. Second, we develop a novel method for extracting Operator Product Expansion (OPE) coefficients from fuzzy sphere data. This method leverages the sensitivity of energy levels to detuning from criticality, providing new insights into level mixing and avoided crossings in finite systems. Our work also includes validation of CPT in a 1+1D Ising model away from the integrable limit.

SCRec: A Scalable Computational Storage System with Statistical Sharding and Tensor-train Decomposition for Recommendation Models

Authors: Jinho Yang, Ji-Hoon Kim, Joo-Young Kim

arXiv ID: 2504.00520 | Date: 2025-04-01

Abstract: Deep Learning Recommendation Models (DLRMs) play a crucial role in delivering personalized content across web applications such as social networking and video streaming. However, with improvements in performance, the parameter size of DLRMs has grown to terabyte (TB) scales, accompanied by memory bandwidth demands exceeding TB/s levels. Furthermore, the workload intensity within the model varies based on the target mechanism, making it difficult to build an optimized recommendation system. In this paper, we propose SCRec, a scalable computational storage recommendation system that can handle TB-scale industrial DLRMs while guaranteeing high bandwidth requirements. SCRec utilizes a software framework that features a mixed-integer programming (MIP)-based cost model, efficiently fetching data based on data access patterns and adaptively configuring memory-centric and compute-centric cores. Additionally, SCRec integrates hardware acceleration cores to enhance DLRM computations, particularly allowing for the high-performance reconstruction of approximated embedding vectors from extremely compressed tensor-train (TT) format. By combining its software framework and hardware accelerators, while eliminating data communication overhead by being implemented on a single server, SCRec achieves substantial improvements in DLRM inference performance. It delivers up to 55.77×\times speedup compared to a CPU-DRAM system with no loss in accuracy and up to 13.35×\times energy efficiency gains over a multi-GPU system.

On Infinite Tensor Networks, Complementary Recovery and Type II Factors

Authors: Wissam Chemissany, Elliott Gesteau, Alexander Jahn, Daniel Murphy, Leo Shaposhnik

arXiv ID: 2504.00096 | Date: 2025-03-31

Abstract: We initiate a study of local operator algebras at the boundary of infinite tensor networks, using the mathematical theory of inductive limits. In particular, we consider tensor networks in which each layer acts as a quantum code with complementary recovery, a property that features prominently in the bulk-to-boundary maps intrinsic to holographic quantum error-correcting codes. In this case, we decompose the limiting Hilbert space and the algebras of observables in a way that keeps track of the entanglement in the network. As a specific example, we describe this inductive limit for the holographic HaPPY code model and relate its algebraic and error-correction features. We find that the local algebras in this model are given by the hyperfinite type II_\infty factor. Next, we discuss other networks that build upon this framework and comment on a connection between type II factors and stabilizer circuits. We conclude with a discussion of MERA networks in which complementary recovery is broken. We argue that this breaking possibly permits a limiting type III von Neumann algebra, making them more suitable ansätze for approximating subregions of quantum field theories.

Spin order, spin excitations, and RIXS spectra of spin-1/2 tetramer chains

Authors: Junli Li, Jun-Qing Cheng, Trinanjan Datta, Dao-Xin Yao

arXiv ID: 2504.00095 | Date: 2025-03-31

Abstract: We investigate the spin dynamics of a 1D spin-1/2 Heisenberg tetramer chain. Employing a combination of Density Matrix Renormalization Group, quantum renormalization group, and perturbation theory techniques, we compute the energy levels and the quantum phase diagram, analyze the phase transitions, and evaluate the LL and KK -edge resonant inelastic x-ray scattering (RIXS) spectrum of fractionalized and collective (single and multi-particle) excitations. Our calculations suggest that the chain can transition between a hidden Z2×Z2Z_2\times Z_2 discrete symmetry preserving tetramer phase and a Haldane phase with non-vanishing string order that breaks the hidden symmetry. These two gapped phases are intervened by an intermediate deconfined quantum critical state comprising of free spins and three-site doublets, which is a gapless critical phase with deconfined spinons. We find that the tetramer chain can support fractionalized (spinon) and collective (triplon and quinton) excitations. In the ferromagnetic intra-tetramer limit, the chain can support a quinton excitation which has a five-fold degenerate excited state. String order parameter calculations suggest CuInVO5_5 to be in a Haldane-like phase whose LL -edge RIXS spectrum can support observable triplon and quinton excitations. We also identify possible two-particle excitations (two-singlon, two-triplon, triplon-quinton, and two-quinton excitations) resulting from the double spin-flip effect in the KK -edge RIXS spectrum.

Bootstrapping the Electronic Structure of Quantum Materials

Authors: Anna O. Schouten, Simon Ewing, David A. Mazziotti

arXiv ID: 2504.02861 | Date: 2025-03-31

Abstract: The last several decades have seen significant advances in the theoretical modeling of materials within the fields of solid-state physics and materials science, but many methods commonly applied to this problem struggle to capture strong electron correlation accurately. Recent widespread interest in quantum materials -- where strong correlation plays a crucial role in the quantum effects governing their behavior -- further highlights the need for theoretical methods capable of rigorously treating such correlation. Here, we present a periodic generalization of variational two-electron reduced density matrix (2-RDM) theory, a bootstrapping-type method that minimizes the ground-state energy as a functional of the 2-RDM without relying on the wavefunction. The 2-RDM is computed directly by semidefinite programming with NN-representability conditions, ensuring accurate treatment of strongly correlated electronic systems. By exploiting translational symmetry, we significantly reduce computational scaling, enabling applications to realistic materials-scale systems. Additionally, we introduce an alternative to conventional energy band structures: natural-orbital occupation-number bands, which, being independent of mean-field assumptions, offer deeper insights into electron correlation effects. We demonstrate the effectiveness of this approach by applying the theory to hydrogen chains, molybdenum disulfide, and nickel oxide, showing that natural-orbital occupation bands correctly capture electronic character in regimes where density functional theory fails. This work represents a major step toward accurately describing the electronic structure of quantum materials using reduced density matrices rather than wavefunctions.

Quantum phase diagram of the extended spin-3/2 Kitaev-Heisenberg model: A DMRG study

Authors: Gui-Xin Liu, Ting-Long Wang, Yi-Fan Jiang

arXiv ID: 2503.24246 | Date: 2025-03-31

Abstract: Recently there has been considerable excitement surrounding the promising realization of high-spin Kitaev material, such as the quasi-2D compound CrI3_3 and CrGeTe3_3. However, the stability of quantum spin liquids (QSL) against single ion anisotropy (SIA) in these materials and the global quantum phase diagram of the extended spin-3/2 Kitaev model with finite SIA remain unclear. In this study, we perform large-scale density matrix renormalization group (DMRG) to explore the quantum phase diagram of the generalized spin-3/2 Kitaev-Heisenberg (K-H) model accompanied with SIA AcA_c. In the Ac=0A_c=0 limit, the spin-3/2 K-H model exhibits a quantum phase diagram similar to that of a spin-1/2 system, including two QSLs around antiferromagnetic and ferromagnetic Kitaev models. For models with finite AcA_c, we map out the quantum phase diagram around two Kitaev points and observe distinct types of in-plane vortex orders developed from these two QSL phases. Interestingly, series of nearly degenerate vortex configurations are discovered in each vortex phases. Using linear spin-wave theory, we demonstrate that these vortex configurations can be understood as a consequence of the quantum correction on a continuous family of degenerate classical states.

Krylov complexity in quantum many-body scars of spin-1 models

Authors: Qingmin Hu, Wen-Yi Zhang, Yunguang Han, Wen-Long You

arXiv ID: 2503.24073 | Date: 2025-03-31

Abstract: Weak ergodicity breaking, particularly through quantum many-body scars (QMBS), has become a significant focus in many-body physics. Krylov state complexity quantifies the spread of quantum states within the Krylov basis and serves as a powerful diagnostic for analyzing nonergodic dynamics. In this work, we study spin-one XXZ magnets and reveal nonergodic behavior tied to QMBS. For the XY model, the nematic Néel state exhibits periodic revivals in Krylov complexity. In the generic XXZ model, we identify spin helix states as weakly ergodicity-breaking states, characterized by low entanglement and nonthermal dynamics. Across different scenarios, the Lanczos coefficients for scarred states display an elliptical pattern, reflecting a hidden SU(2) algebra that enables analytical results for Krylov complexity and fidelity. These findings, which exemplify the rare capability to characterize QMBS analytically, are feasible with current experimental techniques and offer deep insights into the nonergodic dynamics of interacting quantum systems.

Revealing quantum phase string effect in doped Mott-insulator: a tensor network state approach

Authors: Wayne Zheng, Jia-Xin Zhang, Zheng-Yuan Yue, Zheng-Cheng Gu, Zheng-Yu Weng

arXiv ID: 2503.23851 | Date: 2025-03-31

Abstract: We apply the fermionic tensor network (TN) state method to understand the strongly correlated nature in a doped Mott insulator. We conduct a comparative study of the σtσt-JJ model, in which the no-double-occupancy constraint remains unchanged but the quantum phase string effect associated with doped holes is precisely switched off. Thus, the ground state of the σtσt-JJ model can serve as a well-controlled reference state of the standard tt-JJ model. In the absence of phase string, the spin long-range antiferromagnetic (AFM) order is found to be essentially decoupled from the doped holes, and the latter contribute to a Fermi-liquid-like compressibility and a coherent single-particle propagation with a markedly reduced pairing tendency. In contrast, our TN calculations of the tt-JJ model indicate that the AFM order decreases much faster with doping and the single-particle propagation of doped holes gets substantially suppressed, concurrently with a much stronger charge compressibility at small doping and a significantly amplified Cooper pairing tendencies. These findings demonstrate that quantum many-body interference from phase strings plays a pivotal role in the tt-JJ model, mediating long-range entanglement between spin and charge degrees of freedom.

Quantum Methods for Managing Ambiguity in Natural Language Processing

Authors: Jurek Eisinger, Ward Gauderis, Lin de Huybrecht, Geraint A. Wiggins

arXiv ID: 2504.00040 | Date: 2025-03-30

Abstract: The Categorical Compositional Distributional (DisCoCat) framework models meaning in natural language using the mathematical framework of quantum theory, expressed as formal diagrams. DisCoCat diagrams can be associated with tensor networks and quantum circuits. DisCoCat diagrams have been connected to density matrices in various contexts in Quantum Natural Language Processing (QNLP). Previous use of density matrices in QNLP entails modelling ambiguous words as probability distributions over more basic words (the word \texttt{queen}, e.g., might mean the reigning queen or the chess piece). In this article, we investigate using probability distributions over processes to account for syntactic ambiguity in sentences. The meanings of these sentences are represented by density matrices. We show how to create probability distributions on quantum circuits that represent the meanings of sentences and explain how this approach generalises tasks from the literature. We conduct an experiment to validate the proposed theory.

Holographic tensor network for double-scaled SYK

Authors: Kazumi Okuyama

arXiv ID: 2503.23003 | Date: 2025-03-29

Abstract: We construct a holographic tensor network for the double-scaled SYK model (DSSYK). The moment of the transfer matrix of DSSYK can be mapped to the matrix product state (MPS) of a spin chain. By adding the height direction as a holographic direction, we recast the MPS for DSSYK into the holographic tensor network whose building block is a 4-index tensor with the bond dimension three.

Permutation of Tensor-Train Cores for Computing Moments on Stochastic Differential Equations

Authors: Kayo Kinjo, Rihito Sakurai, Tatsuya Kishimoto, Jun Ohkubo

arXiv ID: 2504.10492 | Date: 2025-03-29

Abstract: Tensor networks, particularly the tensor train (TT) format, have emerged as powerful tools for high-dimensional computations in physics and computer science. In solving coupled differential equations, such as those arising from stochastic differential equations (SDEs) via duality relations, ordering the TT cores significantly influences numerical accuracy. In this study, we first systematically investigate how different orderings of the TT cores affect the accuracy of computed moments using the duality relation in stochastic processes. Through numerical experiments on a two-body interaction model, we demonstrate that specific orderings of the TT cores yield lower relative errors, particularly when they align with the underlying interaction structure of the system. Motivated by these findings, we then propose a novel quantitative measure, scorescore, which is defined based on an ordering of the TT cores and an SDE parameter set. While the score is independent of the accuracy of moments to compute by definition, we assess its effectiveness by evaluating the accuracy of computed moments. Our results indicate that orderings that minimize the score tend to yield higher accuracy. This study provides insights into optimizing orderings of the TT cores, which is essential for efficient and reliable high-dimensional simulations of stochastic processes.

Quantum Many-Body Linear Algebra, Hamiltonian Moments, and a Coupled Cluster Inspired Framework

Authors: Yuhang Ai, Huanchen Zhai, Johannes Tölle, Garnet Kin-Lic Chan

arXiv ID: 2503.22908 | Date: 2025-03-28

Abstract: We propose a general strategy to develop quantum many-body approximations of primitives in linear algebra algorithms. As a practical example, we introduce a coupled-cluster inspired framework to produce approximate Hamiltonian moments, and demonstrate its application in various linear algebra algorithms for ground state estimation. Through numerical examples, we illustrate the difference between the ground-state energies arising from quantum many-body linear algebra and those from the analogous many-body perturbation theory. Our results support the general idea of designing quantum many-body approximations outside of perturbation theory, providing a route to new algorithms and approximations.

Solving the Fokker-Planck equation of discretized Dean-Kawasaki models with functional hierarchical tensor

Authors: Xun Tang, Lexing Ying

arXiv ID: 2503.22816 | Date: 2025-03-28

Abstract: We introduce a novel numerical scheme for solving the Fokker-Planck equation of discretized Dean-Kawasaki models with a functional tensor network ansatz. The Dean-Kawasaki model describes density fluctuations of interacting particle systems, and it is a highly singular stochastic partial differential equation. By performing a finite-volume discretization of the Dean-Kawasaki model, we derive a stochastic differential equation (SDE). To fully characterize the discretized Dean-Kawasaki model, we solve the associated Fokker-Planck equation of the SDE dynamics. In particular, we use a particle-based approach whereby the solution to the Fokker-Planck equation is obtained by performing a series of density estimation tasks from the simulated trajectories, and we use a functional hierarchical tensor model to represent the density. To address the challenge that the sample trajectories are supported on a simplex, we apply a coordinate transformation from the simplex to a Euclidean space by logarithmic parameterization, after which we apply a sketching-based density estimation procedure on the transformed variables. Our approach is general and can be applied to general density estimation tasks over a simplex. We apply the proposed method successfully to the 1D and 2D Dean-Kawasaki models. Moreover, we show that the proposed approach is highly accurate in the presence of external potential and particle interaction.

Quantum Approximate Multi-Objective Optimization

Authors: Ayse Kotil, Elijah Pelofske, Stephanie Riedmüller, Daniel J. Egger, Stephan Eidenbenz, Thorsten Koch, Stefan Woerner

arXiv ID: 2503.22797 | Date: 2025-03-28

Abstract: The goal of multi-objective optimization is to understand optimal trade-offs between competing objective functions by finding the Pareto front, i.e., the set of all Pareto optimal solutions, where no objective can be improved without degrading another one. Multi-objective optimization can be challenging classically, even if the corresponding single-objective optimization problems are efficiently solvable. Thus, multi-objective optimization represents a compelling problem class to analyze with quantum computers. In this work, we use low-depth Quantum Approximate Optimization Algorithm to approximate the optimal Pareto front of certain multi-objective weighted maximum cut problems. We demonstrate its performance on an IBM Quantum computer, as well as with Matrix Product State numerical simulation, and show its potential to outperform classical approaches.

Detection of anyon braiding through pump-probe spectroscopy

Authors: Xu Yang, Ryan Buechele, Nandini Trivedi

arXiv ID: 2503.22792 | Date: 2025-03-28

Abstract: We show that the braiding of anyons in a quantum spin liquid leaves a distinct dynamical signature in the nonlinear pump-probe response. Using a combination of exact diagonalization and matrix product state techniques, we study the nonlinear pump-probe response of the toric code in a magnetic field, a model which hosts mobile electric ee and magnetic mm anyonic excitations. While the linear response signal oscillates and decays with time like t1.3\sim t^{-1.3}, the amplitude of the nonlinear signal for χXZZ(3)χ^{(3)}_{XZZ} features a linear-in-time enhancement at early times. The comparison between χXZZ(3)χ^{(3)}_{XZZ}, which involves the non-trivial braiding of ee and mm anyons, and χXXX(3)χ^{(3)}_{XXX} that involves the trivial braiding of the same types of anyons, serves to distinguish the braiding statistics of anyons. We support our analysis by constructing a hard-core anyon model with statistical gauge fields to develop further insights into the time dependence of the pump-probe response. Pump-probe spectroscopy provides a distinctive new probe of quantum spin liquid states, beyond the inconclusive broad features observed in single spin flip inelastic neutron scattering.

The moment polytope of matrix multiplication is not maximal

Authors: Maxim van den Berg, Matthias Christandl, Vladimir Lysikov, Harold Nieuwboer, Michael Walter, Jeroen Zuiddam

arXiv ID: 2503.22633 | Date: 2025-03-28

Abstract: Moment polytopes of tensors, the study of which is deeply rooted in invariant theory, representation theory and symplectic geometry, have found relevance in numerous places, from quantum information (entanglement polytopes) and algebraic complexity theory (GCT program and the complexity of matrix multiplication) to optimization (scaling algorithms). Towards an open problem in algebraic complexity theory, we prove separations between the moment polytopes of matrix multiplication tensors and unit tensors. As a consequence, we find that matrix multiplication moment polytopes are not maximal, i.e. are strictly contained in the corresponding Kronecker polytope. As another consequence, we obtain a no-go result for a natural operational characterization of moment polytope inclusion in terms of asymptotic restriction. We generalize the separation and non-maximality to moment polytopes of iterated matrix multiplication tensors. Our result implies that tensor networks where multipartite entanglement structures beyond two-party entanglement are allowed can go beyond projected entangled-pair states (PEPS) in terms of expressivity. Our proof characterizes membership of uniform points in moment polytopes of tensors, and establishes a connection to polynomial multiplication tensors via the minrank of matrix subspaces. As a result of independent interest, we extend these techniques to obtain a new proof of the optimal border subrank bound for matrix multiplication.

Charge creation via quantum tunneling in one-dimensional Mott insulators: A numerical study of the extended Hubbard model

Authors: Thomas Hansen, Lars Bojer Madsen, Yuta Murakami

arXiv ID: 2503.22481 | Date: 2025-03-28

Abstract: Charge creation via quantum tunneling, i.e. dielectric breakdown, is one of the most fundamental and significant phenomena arising from strong light(field)-matter coupling. In this work, we conduct a systematic numerical analysis of quantum tunneling in one-dimensional Mott insulators described by the extended (UU-VV) Hubbard model. We discuss the applicability of the analytical formula for doublon-holon (DH) pair production, previously derived for the one-dimensional Hubbard model, which highlights the relationship between the tunneling threshold, the charge gap, and the correlation length. We test the formulas ability to predict both DH pair production and energy increase rate. Using tensor-network-based approaches, we demonstrate that the formula provides accurate predictions in the absence of excitonic states facilitated by the nearest-neighbor interaction VV. However, when excitonic states emerge, the formula more accurately describes the rate of energy increase than the DH pair creation rate and in both cases gets improved by incorporating the exciton energy as the effective gap.

Spontaneous symmetry breaking with type-B Goldstone modes in the SO(2s+12s+1) ferromagnetic model: an entanglement perspective

Authors: Qian-Qian Shi, Huan-Qiang Zhou, Murray T. Batchelor, Ian P. McCulloch

arXiv ID: 2503.22468 | Date: 2025-03-28

Abstract: Spontaneous symmetry breaking with type-B Goldstone modes is investigated in the SO(2s+12s+1) ferromagnetic model. A set of orthonormal basis states in the ground state subspace are constructed, which admit an exact Schmidt decomposition, exposing self-similarities in real space of an abstract fractal underlying the ground state subspace. Focusing on the SO(5) and the SO(6) ferromagnetic spin chains as illustrative examples, finite system-size scaling analysis of the entanglement entropy for this set of orthonormal basis states confirms that the entanglement entropy scales logarithmically with block size in the thermodynamic limit. The prefactor in front of the logarithm is half the number of type-B Goldstone modes NBN_B, which is identified as the fractal dimension dfd_f for these orthonormal basis states. For the SO(2s+12s+1) ferromagnetic model NB=df=sN_B = d_f =s for integer ss and NB=df=s+1/2N_B = d_f =s+1/2 for half-odd-integer ss.

Taking the temperature of quantum many-body scars

Authors: Phillip C. Burke, Shane Dooley

arXiv ID: 2503.21884 | Date: 2025-03-27

Abstract: A quantum many-body scar is an eigenstate of a chaotic many-body Hamiltonian that exhibits two seemingly incongruous properties: its energy eigenvalue corresponds to a high temperature, yet its entanglement structure resembles that of low-temperature eigenstates, such as ground states. Traditionally, a temperature is assigned to an energy \emph{eigenvalue} through the textbook canonical temperature-energy relationship. However, in this work, we use the \emph{eigenstate subsystem temperature} -- a recently developed quantity that assigns a temperature to an energy eigenstate, based on the structure of its reduced density matrix. For a thermal state, the eigenstate subsystem temperature is approximately equal to its canonical temperature. Given that quantum many-body scars have a ground-state-like entanglement structure, it is not immediately clear that their eigenstate subsystem temperature would be close to their canonical temperature. Surprisingly, we find that this is the case: the quantum many-body scars have approximate ``knowledge'' of their position in the spectrum encoded within their state structure.

Extracting Coupling-Mode Spectral Densities with Two-Dimensional Electronic Spectroscopy

Authors: Roosmarijn de Wit, Jonathan Keeling, Brendon W. Lovett, Alex W. Chin

arXiv ID: 2503.21685 | Date: 2025-03-27

Abstract: Methods for reconstructing the spectral density of a vibrational environment from experimental data can yield key insights into the impact of the environment on molecular function. Although such experimental methods exist, they generally only access vibrational modes that couple diagonally to the electron system. Here we present a method for extracting the spectral density of modes that couple to the transition between electronic states, using two-dimensional electronic spectroscopy. To demonstrate this, we use a process-tensor method that can simulate two-dimensional electronic spectroscopy measurements in a numerically exact way. To explain how the extraction works, we also derive an approximate analytical solution, which illustrates that the non-Markovianity of the environment plays an essential role in the existence of the simulated signal.

Prethermalization by Random Multipolar Driving on a 78-Qubit Superconducting Processor

Authors: Zheng-He Liu, Yu Liu, Gui-Han Liang, Cheng-Lin Deng, Keyang Chen, Yun-Hao Shi, Tian-Ming Li, Lv Zhang, Bing-Jie Chen, Cai-Ping Fang, Da'er Feng, Xu-Yang Gu, Yang He, Kaixuan Huang, Hao Li, Hao-Tian Liu, Li Li, Zheng-Yang Mei, Zhen-Yu Peng, Jia-Cheng Song, Ming-Chuan Wang, Shuai-Li Wang, Ziting Wang, Yongxi Xiao, Minke Xu, Yue-Shan Xu, Yu Yan, Yi-Han Yu, Wei-Ping Yuan, Jia-Chi Zhang, Jun-Jie Zhao, Kui Zhao, Si-Yun Zhou, Zheng-An Wang, Xiaohui Song, Ye Tian, Florian Mintert, Johannes Knolle, Roderich Moessner, Yu-Ran Zhang, Pan Zhang, Zhongcheng Xiang, Dongning Zheng, Kai Xu, Hongzheng Zhao, Heng Fan

arXiv ID: 2503.21553 | Date: 2025-03-27

Abstract: Time-dependent drives hold the promise of realizing non-equilibrium many-body phenomena that are absent in undriven systems. Yet, drive-induced heating normally destabilizes the systems, which can be parametrically suppressed in the high-frequency regime by using periodic (Floquet) drives. It remains largely unknown to what extent highly controllable quantum simulators can suppress heating in non-periodically driven systems. Using the 78-qubit superconducting quantum processor, Chuang-tzu 2.0, we report the experimental observation of long-lived prethermal phases in many-body systems with tunable heating rates, driven by structured random protocols, characterized by nn-multipolar temporal correlations. By measuring both the particle imbalance and subsystem entanglement entropy, we monitor the entire heating process over 1,000 driving cycles and observe the existence of the prethermal plateau. The prethermal lifetime is `doubly tunable': one way by driving frequency, the other by multipolar order; it grows algebraically with the frequency with the universal scaling exponent 2n+12n{+}1. Using quantum state tomography on different subsystems, we demonstrate a non-uniform spatial entanglement distribution and observe a crossover from area-law to volume-law entanglement scaling. With 78 qubits and 137 couplers in a 2D configuration, the entire far-from-equilibrium heating dynamics are beyond the reach of simulation using tensor-network numerical techniques. Our work highlights superconducting quantum processors as a powerful platform for exploring universal scaling laws and non-equilibrium phases of matter in driven systems in regimes where classical simulation faces formidable challenges.

F-INR: Functional Tensor Decomposition for Implicit Neural Representations

Authors: Sai Karthikeya Vemuri, Tim Büchner, Joachim Denzler

arXiv ID: 2503.21507 | Date: 2025-03-27

Abstract: Implicit Neural Representations (INRs) model signals as continuous, differentiable functions. However, monolithic INRs scale poorly with data dimensionality, leading to excessive training costs. We propose F-INR, a framework that addresses this limitation by factorizing a high-dimensional INR into a set of compact, axis-specific sub-networks based on functional tensor decomposition. These sub-networks learn low-dimensional functional components that are then combined via tensor operations. This factorization reduces computational complexity while additionally improving representational capacity. F-INR is both architecture- and decomposition-agnostic. It integrates with various existing INR backbones (e.g., SIREN, WIRE, FINER, Factor Fields) and tensor formats (e.g., CP, TT, Tucker), offering fine-grained control over the speed-accuracy trade-off via the tensor rank and mode. Our experiments show F-INR accelerates training by up to 20×20\times and improves fidelity by over \num{6.0} dB PSNR compared to state-of-the-art INRs. We validate these gains on diverse tasks, including image representation, 3D geometry reconstruction, and neural radiance fields. We further show F-INR's applicability to scientific computing by modeling complex physics simulations. Thus, F-INR provides a scalable, flexible, and efficient framework for high-dimensional signal modeling. Project page: https://f-inr.github.io

Dynamic scaling and Family-Vicsek universality in SU(N)SU(N) quantum spin chains

Authors: Cătălin Paşcu Moca, Balázs Dóra, Doru Sticlet, Angelo Valli, Tomaž Prosen, Gergely Zaránd

arXiv ID: 2503.21454 | Date: 2025-03-27

Abstract: The Family-Vicsek scaling is a fundamental framework for understanding surface growth in non-equilibrium classical systems, providing a universal description of temporal surface roughness evolution. While universal scaling laws are well established in quantum systems, the applicability of Family-Vicsek scaling in quantum many-body dynamics remains largely unexplored. Motivated by this, we investigate the infinite-temperature dynamics of one-dimensional SU(N)SU(N) spin chains, focusing on the well-known SU(2)SU(2) XXZ model and the SU(3)SU(3) Izergin-Korepin model. We compute the quantum analogue of classical surface roughness using the second cumulant of spin fluctuations and demonstrate universal scaling with respect to time and subsystem size. By systematically breaking global SU(N)SU(N) symmetry and integrability, we identify distinct transport regimes characterized by the dynamical exponent zz: (i) ballistic transport with z=1z=1, (ii) superdiffusive transport with the Kardar-Parisi-Zhang exponent z=3/2z=3/2, and (iii) diffusive transport with the Edwards-Wilkinson exponent z=2z=2. Notably, breaking integrability always drives the system into the diffusive regime. Our results demonstrate that Family-Vicsek scaling extends beyond classical systems, holding universally across quantum many-body models with SU(N)SU(N) symmetry.

Exponential quantum speedups in quantum chemistry with linear depth

Authors: Oskar Leimkuhler, K. Birgitta Whaley

arXiv ID: 2503.21041 | Date: 2025-03-26

Abstract: We prove classical simulation hardness, under the generalized PNP\mathsf{P}\neq\mathsf{NP} conjecture, for quantum circuit families with applications in near-term chemical ground state estimation. The proof exploits a connection to particle number conserving matchgate circuits with fermionic magic state inputs, which are shown to be universal for quantum computation under post-selection, and are therefore not classically simulable in the worst case, in either the strong (multiplicative) or weak (sampling) sense. We apply this result to quantum multi-reference methods designed for near-term hardware by ruling out certain dequantization strategies for computing the off-diagonal matrix elements. We demonstrate these quantum speedups for two choices of reference state that incorporate both static and dynamic correlations to model the electronic eigenstates of molecular systems: orbital-rotated matrix product states, which are preparable in linear depth, and generalized unitary coupled-cluster with single and double excitations, for which computing the off-diagonal matrix elements is BQP\mathsf{BQP}-complete for any polynomial depth. In each case we discuss the implications for achieving exponential quantum advantage in quantum chemistry on near-term hardware.

Solvable Quantum Circuits in Tree+1 Dimensions

Authors: Oliver Breach, Benedikt Placke, Pieter W. Claeys, S. A. Parameswaran

arXiv ID: 2503.20927 | Date: 2025-03-26

Abstract: We devise tractable models of unitary quantum many-body dynamics on tree graphs, as a first step towards a deeper understanding of dynamics in non-Euclidean spaces. To this end, we first demonstrate how to construct strictly local quantum circuits that preserve the symmetries of trees, such that their dynamical light cones grow isotropically. For trees with coordination number z, such circuits can be built from z-site gates. We then introduce a family of gates for which the dynamics is exactly solvable; these satisfy a set of constraints that we term 'tree-unitarity'. Notably, tree-unitarity reduces to the previously-established notion of dual-unitarity for z = 2, when the tree reduces to a line. Among the unexpected features of tree-unitarity is a trade-off between 'maximum butterfly velocity' dynamics of out-of-time-order correlators and the existence of non-vanishing correlation functions in multiple directions, a tension absent in one-dimensional dual-unitary models and their Euclidean generalizations. We connect the existence of (a wide class of) solvable dynamics with non-maximal butterfly velocity directly to a property of the underlying circuit geometry called δδ-hyperbolicity, and argue that such dynamics can only arise in non-Euclidean geometries. We give various examples of tree-unitary gates, discuss dynamical correlations, out-of-time-order correlators, and entanglement growth, and show that the kicked Ising model on a tree is a physically-motivated example of maximum-velocity tree-unitary dynamics.

Quantum Coherence of Topologically Frustrated Spin Chains

Authors: S. B. Kožić, G. Torre, K. Delić, F. Franchini, S. M. Giampaolo

arXiv ID: 2503.20874 | Date: 2025-03-26

Abstract: The study of entanglement and magic properties in topologically frustrated systems suggests that, in the thermodynamic limit, these quantities decompose into two distinct contributions. One is determined by the specific nature of the model and its Hamiltonian, and another arises from topological frustration itself, resulting in being independent of the Hamiltonian's parameters. In this work, we test the generality of this picture by investigating an additional quantum resource, namely quantum coherence, in two different models where topological frustration is induced through an appropriate choice of boundary conditions. Our findings reveal a perfect analogy between the behavior of quantum coherence and that of other quantum resources, particularly magic, providing further evidence in support of the universality of this picture and the topological nature of this source of frustration.

Digital quantum magnetism at the frontier of classical simulations

Authors: Reza Haghshenas, Eli Chertkov, Michael Mills, Wilhelm Kadow, Sheng-Hsuan Lin, Yi-Hsiang Chen, Chris Cade, Ido Niesen, Tomislav Begušić, Manuel S. Rudolph, Cristina Cirstoiu, Kevin Hemery, Conor Mc Keever, Michael Lubasch, Etienne Granet, Charles H. Baldwin, John P. Bartolotta, Matthew Bohn, Julia Cline, Matthew DeCross, Joan M. Dreiling, Cameron Foltz, David Francois, John P. Gaebler, Christopher N. Gilbreth, Johnnie Gray, Dan Gresh, Alex Hall, Aaron Hankin, Azure Hansen, Nathan Hewitt, Ross B. Hutson, Mohsin Iqbal, Nikhil Kotibhaskar, Elliot Lehman, Dominic Lucchetti, Ivaylo S. Madjarov, Karl Mayer, Alistair R. Milne, Steven A. Moses, Brian Neyenhuis, Gunhee Park, Boris Ponsioen, Michael Schecter, Peter E. Siegfried, David T. Stephen, Bruce G. Tiemann, Maxwell D. Urmey, James Walker, Andrew C. Potter, David Hayes, Garnet Kin-Lic Chan, Frank Pollmann, Michael Knap, Henrik Dreyer, Michael Foss-Feig

arXiv ID: 2503.20870 | Date: 2025-03-26

Abstract: The utility of near-term quantum computers for simulating realistic quantum systems hinges on the stability of digital quantum matter--realized when discrete quantum gates approximate continuous time evolution--and whether it can be maintained at system sizes and time scales inaccessible to classical simulations. Here, we use Quantinuum's H2 quantum computer to simulate digitized dynamics of the quantum Ising model and observe the emergence of Floquet prethermalization on timescales where accurate simulations using current classical methods are extremely challenging (if feasible at all). In addition to confirming the stability of dynamics subject to achievable digitization errors, we show direct evidence of the resultant local equilibration by computing diffusion constants associated with an emergent hydrodynamic description of the dynamics. Our results were enabled by continued advances in two-qubit gate quality (native partial entangler fidelities of 99.94(1)%) that allow us to access circuit volumes of over 2000 two-qubit gates. This work establishes digital quantum computers as powerful tools for studying continuous-time dynamics and demonstrates their potential to benchmark classical heuristics in a regime of scale and complexity where no known classical methods are both efficient and trustworthy.

BaCo2_2(AsO4_4)2_2: Strong Kitaev, After All

Authors: Pavel A. Maksimov, Shengtao Jiang, L. P. Regnault, A. L. Chernyshev

arXiv ID: 2503.20859 | Date: 2025-03-26

Abstract: The inelastic neutron scattering results and their analysis unequivocally point to a dominant Kitaev interaction in the honeycomb-lattice cobaltate BaCo2_2(AsO4_4)2_2. Our anisotropic-exchange model closely describes allall available neutron scattering data in the material's field-polarized phase. The density-matrix renormalization group results for our model are in close accord with the unusual double-zigzag magnetic order and the low in-plane saturation field of BaCo2_2(AsO4_4)2_2.

Orbital optimization of large active spaces via AI-accelerators

Authors: Örs Legeza, Andor Menczer, Ádám Ganyecz, Miklós Antal Werner, Kornél Kapás, Jeff Hammond, Sotiris S. Xantheas, Martin Ganahl, Frank Neese

arXiv ID: 2503.20700 | Date: 2025-03-26

Abstract: We present an efficient orbital optimization procedure that combines the highly GPU accelerated, spin-adapted density matrix renormalization group (DMRG) method with the complete active space self-consistent field (CAS-SCF) approach for quantum chemistry implemented in the ORCA program package. Leveraging the computational power of the latest generation of Nvidia GPU hardware, we perform CAS-SCF based orbital optimizations for unprecedented CAS sizes of up to 82 electrons in 82 orbitals [CAS(82,82)] in molecular systems comprising of active spaces sizes of hundreds of electrons in thousands of orbitals. For both the NVIDIA DGX-A100 and DGX-H100 hardware, we provide a detailed scaling and error analysis of our DMRG-SCF approach for benchmark systems consisting of polycyclic aromatic hydrocarbons and iron-sulfur complexes of varying sizes. Our efforts demonstrate for the first time that highly accurate DMRG calculations at large bond dimensions are critical for obtaining reliably converged CAS-SCF energies. For the more challenging iron-sulfur benchmark systems, we furthermore find the optimized orbitals of a converged CAS-SCF calculation to depend more sensitively on the DMRG parameters than those for the polycyclic aromatic hydrocarbons. The ability to obtain converged CAS-SCF energies and orbitals for active spaces of such large sizes within days reduces the challenges of including the appropriate orbitals into the CAS or selecting the correct minimal CAS, and may open up entirely new avenues for tackling strongly correlated molecular systems.

Accurate Gauge-Invariant Tensor Network Simulations for Abelian Lattice Gauge Theory in (2+1)D: ground state and real-time dynamics

Authors: Yantao Wu, Wen-Yuan Liu

arXiv ID: 2503.20566 | Date: 2025-03-26

Abstract: We propose a novel tensor network method to achieve accurate and efficient simulations of Abelian lattice gauge theories (LGTs) in (2+1)D for both ground state and real-time dynamics. The first key is to identify a gauge canonical form (GCF) of gauge-invariant tensor network states, which already simplifies existing algorithms for (1+1)D LGTs. The second key is to employ the GCF of projected entangled-pair state (PEPS) combining with variational Monte Carlo (VMC), enabling efficient computations for (2+1)D LGTs. We demonstrate the versatile capability of this approach for accurate ground state simulation of pure Z2Z_2, Z3Z_3 and Z4Z_4 gauge theory, odd-Z2Z_2 gauge theories, and Z2Z_2 gauge theory coupled to hard-core bosons, on square lattices up to 32×3232 \times 32. Furthermore, we demonstrate that it allows for accurate simulations of real-time dynamics up to long-time, exemplified by the dynamics of elementary excitations of the deconfined Z2Z_2 gauge field on a 10×1010\times10 lattice. This is also the first example of using VMC to simulate the real-time dynamics of PEPS, whose impact may extend beyond gauge theory.

Symmetry resolved out-of-time-order correlators of Heisenberg spin chains using projected matrix product operators

Authors: Martina Gisti, David J. Luitz, Maxime Debertolis

arXiv ID: 2503.20327 | Date: 2025-03-26

Abstract: We extend the concept of operator charge in the context of an abelian U (1) symmetry and apply this framework to symmetry-preserving matrix product operators (MPOs), enabling the description of operators projected onto specific sectors of the corresponding symmetry. Leveraging this representation, we study the effect of interactions on the scrambling of information in an integrable Heisenberg spin chain, by controlling the number of particles. Our focus lies on out-of-time order correlators (OTOCs) which we project on sectors with a fixed number of particles. This allows us to link the non-interacting system to the fully-interacting one by allowing more and more particle to interact with each other, keeping the interaction parameter fixed. While at short times, the OTOCs are almost not affected by interactions, the spreading of the information front becomes gradually faster and the OTOC saturate at larger values as the number of particle increases. We also study the behavior of finite-size systems by considering the OTOCs at times beyond the point where the front hits the boundary of the system. We find that in every sector with more than one particle, the OTOCs behave as if the local operator was rotated by a random unitary matrix, indicating that the presence of boundaries contributes to the maximal scrambling of local operators.

Variational M-Partite Geometric Entanglement Algorithm

Authors: Vahid Azimi-Mousolou, Prashant Singh

arXiv ID: 2503.20056 | Date: 2025-03-25

Abstract: Variational quantum algorithms have emerged as a powerful tool for harnessing the potential of near-term quantum devices to address complex challenges across quantum science and technology. Yet, the robust and scalable quantification of entanglement in many-body quantum systems remains a significant challenge, crucial for both advancing theoretical understanding and enabling practical applications. In this work, we propose a variational quantum algorithm to evaluate the MM-partite geometric entanglement across arbitrary partitions of an NN-qubit system into MM parties. By constructing tailored variational ansatz circuits for both single- and multi-qubit parties, we optimize the overlap between a target quantum state and an MM-partite variational separable state. This method provides a flexible and scalable approach for characterizing arbitrary MM-partite entanglement in complex quantum systems of a given dimension. The accuracy of the proposed method is assessed by reproducing known analytical results. We further demonstrate its capability to evaluate entanglement among MM parties for any given conventional or unconventional partitions of one- and two-dimensional spin systems, both near and at a quantum critical point. Our results establish the versatility of the variational approach in capturing different types of entanglement in various quantum systems, surpassing the capabilities of existing methods. Our approach offers a powerful methodology for advancing research in quantum information science, condensed matter physics, and quantum field theory. Additionally, we discuss its advantages, highlighting its adaptability to diverse system architectures in the context of near-term quantum devices.

Comment on: "Dynamics of disordered quantum systems with two- and three-dimensional tensor networks" arXiv:2503.05693

Authors: Andrew D. King, Alberto Nocera, Marek M. Rams, Jacek Dziarmaga, Jack Raymond, Nitin Kaushal, Anders W. Sandvik, Gonzalo Alvarez, Juan Carrasquilla, Marcel Franz, Mohammad H. Amin

arXiv ID: 2504.06283 | Date: 2025-03-25

Abstract: In a recent preprint [1] (arXiv:2503.05693), Tindall et al. presented impressive classical simulations of quantum dynamics using tensor networks. Their methods represent a significant improvement in the classical state of the art, and in some cases show lower errors than recent simulations of quantum dynamics using a quantum annealer [2] (King et al., Science, eado6285, 2025). However, of the simulations in Ref. [2], Ref. [1] did not attempt the most complex lattice geometry, nor reproduce the largest simulations in 3D lattices, nor simulate the longest simulation times, nor simulate the low-precision ensembles in which correlations grow the fastest, nor produce the full-state and fourth-order observables produced by Ref. [2]. Thus this work should not be misinterpreted as having overturned the claim of Ref. [2]: the demonstration of quantum simulations beyond the reach of classical methods. Rather, these classical advances narrow the parameter space in which beyond-classical computation has been demonstrated. In the near future these classical methods can be combined with quantum simulations to help sharpen the boundary between classical and quantum simulability.

Single-band Triangular Lattice Hubbard Model with Tunable Anisotropy from Twisted Diamond Homobilayers

Authors: Wen Sun, Chuyi Tuo, Hong Yao

arXiv ID: 2503.19829 | Date: 2025-03-25

Abstract: The ground-state properties of the single-band triangular lattice Hubbard model with hopping anisotropy and strong interactions remain elusive so far. Here we show that twisted diamond homobilayers with band extrema at YY valley can realize weakly-coupled chains with quasi-1D band structure; applying displacement field generates interchain hopping, transforming this quasi-1D system into a 2D one. The low-energy physics can be described by localized Wannier functions on the triangular lattice with tunable hopping anisotropy, providing a promising platform for studying the anisotropic triangular lattice Hubbard model. We further employ density matrix renormalization group to study this model with interaction U=10tU=10t and anisotropy 0.5t/t1.50.5\leq t'/t\leq 1.5 at half filling, and obtain a rich ground state phase diagram, including a chiral spin liquid phase, non-magnetic phases, and a Néel antiferromagnetic phase. This work provides a first realization of displacement-field tuned anisotropy in a single-band triangular Hubbard model within moiré systems, establishing them as a promising platform to investigate intriguing correlated physics with tunable anisotropy.

Emergent Pair Density Wave Order Across a Lifshitz Transition

Authors: Luhang Yang, Elbio Dagotto, Adrian E. Feiguin

arXiv ID: 2503.19761 | Date: 2025-03-25

Abstract: We numerically investigate the telltale signs of pair-density-wave order (PDW) in the Kondo-Heisenberg chain by focusing on the momentum resolved spectrum in different parameter regimes. Density matrix renormalization group calculations reveal that this phase is characterized by a dispersion with two minima and four Fermi points, indicating the emergence of an effective next-nearest-neighbor hopping that arises as a second-order effect to avoid magnetic frustration. The pairs appear in the spectrum as in-gap bound states with weight concentrated in the hole pockets. The low-energy physics can be understood by means of a generalized t-J model with next-nearest-neighbor hopping. Our results offer a guide for searching for experimental signatures, and for other models that can realize PDW physics.

Dynamics of one-dimensional spin models via complex-time evolution of tensor networks

Authors: Jeong Hyeok Cha, Hyun-Yong Lee, Heung-Sik Kim

arXiv ID: 2503.19269 | Date: 2025-03-25

Abstract: Studying the real-time dynamics of strongly correlated systems poses significant challenges, which have recently become more manageable thanks to advances in density matrix renormalization group (DMRG) and tensor network methods. A notable development in this area is the introduction of a complex-time evolution scheme for tensor network states, originally suggested for solving Anderson impurity model and designed to suppress the growth of entanglement under time evolution. In this study, we employ the complex-time evolution scheme to investigate the dynamics of one-dimensional spin systems, specifically the transverse-field Ising model (TFIM) and the XXZ model. Our analysis revisits the dynamic critical exponent zz of the TFIM and explores the dynamical structure factor in both gapped and gapless states of the XXZ model. Importantly, the complex-time evolution reproduces the results of real-time evolution while mitigating the rapid growth of quantum entanglement typically associated with the latter. These results demonstrate that the combination of complex-time evolution and extrapolation provides a robust and efficient framework for studying the dynamics of complex quantum systems, enabling more comprehensive insights into their behavior.

Tensor-network study of the roughening transition in a (2 + 1)D Z2\mathbb{Z}_2 lattice gauge theory with matter

Authors: Wen-Tao Xu, Michael Knap, Frank Pollmann

arXiv ID: 2503.19027 | Date: 2025-03-24

Abstract: Within the confined phase of (2+1)D lattice gauge theories a roughening transition arises between a weakly confined regime with floppy string excitations and a strongly confined regime with stiff string excitations. In this work, we use an infinite Density Matrix Renormalization Group (iDMRG) algorithm to quantitatively characterize the properties of confined strings. To this end, we stabilize the state with a string excitation by 't Hooft loop operators. While for zero gauge-matter coupling we can use bare 't Hooft loop operators to do so, for finite gauge-matter coupling we have to transform them to emergent ones, which we achieve with an adiabatic protocol. By analyzing the scaling of both a novel order parameter and the entanglement entropy, our approach allows us to accurately determine the roughening transition, even at finite gauge-matter coupling.

Simulation of Fermionic circuits using Majorana Propagation

Authors: Aaron Miller, Joachim Favre, Zoë Holmes, Özlem Salehi, Rahul Chakraborty, Anton Nykänen, Zoltán Zimborás, Adam Glos, Guillermo García-Pérez

arXiv ID: 2503.18939 | Date: 2025-03-24

Abstract: We introduce Majorana Propagation, an algorithmic framework for the classical simulation of Fermionic circuits. Inspired by Pauli Propagation, Majorana Propagation operates by applying successive truncations throughout the Heisenberg evolution of the observable. We identify monomial length as an effective truncation strategy for typical, unstructured circuits by proving that high-length Majorana monomials are exponentially unlikely to contribute to expectation values and the backflow of high-length monomials to lower-length monomials is quadratically suppressed. We provide performance guarantees by proving analytically that approximation errors decrease exponentially with the truncation threshold and that only polynomial resources are required to compute the expectation value of observables up to a fixed error for an ensemble of circuits relevant to quantum chemistry. Majorana Propagation can be used either independently, or in conjunction with quantum hardware, to simulate Fermionic systems relevant to quantum chemistry and condensed matter. We exemplify this by using Majorana Propagation to find circuits that approximate ground states for strongly correlated systems of up to 52 Fermionic modes. Our results indicate that Majorana Propagation is orders of magnitude faster and more accurate than state-of-the-art tensor-network-based circuit simulators.

A brief note on the G2_2 Affleck-Kennedy-Lieb-Tasaki chain

Authors: Hosho Katsura, Dirk Schuricht

arXiv ID: 2503.18885 | Date: 2025-03-24

Abstract: We consider the valence bond solid (VBS) state built of singlet pairs of fundamental representations and projected onto adjoint representations of the exceptional Lie group G2_2. The two-point correlation function in the VBS state is non-vanishing only for nearest neighbours, but possesses finite string order. We construct a parent Hamiltonian for the VBS state, which constitutes the G2_2 analog of the famous AKLT chain.

Efficient QR-Based CP Decomposition Acceleration via Restructured Dimension Tree and Customized Extrapolation

Authors: Wenchao Xie, Jiawei Xu, Zheng Peng, Qingsong Wang

arXiv ID: 2503.18759 | Date: 2025-03-24

Abstract: The canonical polyadic (CP) decomposition is one of the most widely used tensor decomposition techniques. The conventional CP decomposition algorithm combines alternating least squares (ALS) with the normal equation. However, the normal equation is susceptible to numerical ill-conditioning, which can adversely affect the decomposition results. To mitigate this issue, ALS combined with QR decomposition has been proposed as a more numerically stable alternative. Although this method enhances stability, its iterative process involves tensor-times-matrix (TTM) operations, which typically result in higher computational costs. To reduce this cost, we propose restructured dimension tree, which increases the reuse of intermediate tensors and reduces the number of TTM operations. Compared with the standard dimension tree structure, this dimension tree structure can reduce the computational complexity of TTM operations for tensors of any order by 33\%. Additionally, we introduce a customized extrapolation strategy in the CP-ALS-QR algorithm, leveraging the unique structure of the matrix Q0\mathbf{Q}_0 to further accelerate convergence. By integrating these two techniques, we propose a novel CP decomposition algorithm that significantly improves iteration efficiency, achieving up to twofold acceleration on datasets with certain specific structures. Numerical experiments on five real-world datasets show that, compared with the baseline algorithm, our proposed algorithm improves iteration efficiency while simultaneously enhancing fitting accuracy.

Random quantum Ising model with three-spin couplings

Authors: Ferenc Iglói, Yu-Cheng Lin

arXiv ID: 2503.18690 | Date: 2025-03-24

Abstract: We apply a real-space block renormalization group approach to study the critical properties of the random transverse-field Ising spin chain with multispin interactions. First we recover the known properties of the traditional model with two-spin interactions by applying the renormalization approach for arbitrary size of the block. For the model with three-spin couplings we calculate the critical point and demonstrate that the phase transition is controlled by an infinite disorder fixed point. We have determined the typical correlation-length critical exponent, which seems to be different from that of the random transverse Ising chain with nearest-neighbor couplings. Thus this model represents a new infinite disorder universality class.

Screening in Hubbard models with long-range interactions

Authors: Florian Gebhard, Kevin Bauerbach, Örs Legeza

arXiv ID: 2503.18639 | Date: 2025-03-24

Abstract: We provide solid evidence for the long-standing presumption that model Hamiltonians with short-range interactions faithfully reproduce the physics of the long-range Coulomb interaction in real materials. For this aim, we address a generic Hubbard model that captures the quantum phase transitions between metal, Mott insulator, and charge-density-wave insulator, in the absence of Fermi-surface nesting. By comparing the quantum phase diagrams for the 1/r1/r-Hubbard model on a half-filled chain with nearest-neighbor and 1/r1/r-long-range interactions, we argue that the inclusion of long-range interactions is not crucial for a proper description of interacting many-electron systems. To this end, we employ the Density Matrix Renormalization Group method on finite lattices and antiperiodic boundary conditions to determine the quantum phase transitions between the metallic Luttinger liquid for weak interactions, the Mott-Hubbard insulator for dominant on-site interactions, and the charge-density wave insulator for dominant inter-site interactions. The two phase diagrams qualitatively agree inasmuch as the quantum phase transitions are continuous in both cases. Moreover, simple Hartree-Fock theory and the atomic limit provide renormalization factors that allow us to quantitatively map the two phase diagrams onto each other. As a practical advantage, our findings imply that computational efforts can be reduced tremendously by using models with short-range interactions only.

Exploring the Finite-Temperature Behavior of Rydberg Atom Arrays: A Tensor Network Approach

Authors: Yuzhou Han, Hao Zhang, Lixin He

arXiv ID: 2503.18413 | Date: 2025-03-24

Abstract: Rydberg atom arrays have emerged as a powerful platform for experimental research and a challenging subject for theoretical investigation in quantum science. In this study, we investigate the finite-temperature properties of two-dimensional square-lattice Rydberg atom arrays using the projected entangled pair states (PEPS) method. By analyzing the thermal behavior of systems in the checkerboard and striated phases, we extract critical exponents and identify phase transition characteristics. Our results confirm that the checkerboard phase transition belongs to the 2D Ising universality class, while the striated phase exhibits critical exponents that deviate from known universality classes, possibly due to finite-size effects. These findings provide theoretical insights into the thermal stability of quantum phases in Rydberg atom arrays and offer valuable guidance for future experimental efforts.

A Promising Method for Strongly Correlated Electrons in Two Dimensions: Gutzwiller-Guided Density Matrix Renormalization Group

Authors: Hui-Ke Jin, Rong-Yang Sun, Hong-Hao Tu, Yi Zhou

arXiv ID: 2503.18374 | Date: 2025-03-24

Abstract: The study of strongly correlated electron systems remains a fundamental challenge in condensed matter physics, particularly in two-dimensional (2D) systems hosting various exotic phases of matter including quantum spin liquids, unconventional superconductivity, and topological orders. Although Density Matrix Renormalization Group (DMRG) has established itself as a pillar for simulating one-dimensional quantum systems, its application to 2D systems has long been hindered by the notorious ``local minimum'' issues. Recent methodological breakthroughs have addressed this challenge by incorporating Gutzwiller-projected wavefunctions as initial states for DMRG simulations. This hybrid approach, referred to as DMRG guided by Gutzwiller-projected wave functions (or Gutzwiller-guided DMRG), has demonstrated remarkable improvements in accuracy, efficiency, and the ability to explore exotic quantum phases such as topological orders. This review examines the theoretical underpinnings of this approach, details key algorithmic developments, and showcases its applications in recent studies of 2D quantum systems.

Emergent supercounterfluid and quantum phase diagram of two-component interacting bosons in one-dimensional optical lattice

Authors: Saisai He, Yang Liu, Bin Xi, Hong-Gang Luo, Qiang Luo, Jize Zhao

arXiv ID: 2503.18154 | Date: 2025-03-23

Abstract: Motivated by a recent experiment that realizes nearest-neighbor dipolar couplings in an optical lattice [C. Lagoin, et al.\textit{et al.}, Nature 609\textbf{609}, 485 (2022)], we study a one-dimensional version of the two-component extended Bose-Hubbard model via the density-matrix renormalization group method. By using the nearest-neighbor and on-site interaction parameters from the experiment, we start by mapping the quantum phase diagram in the hopping parameters tA-tBt_{A}\text{-}t_{B} plane with boson densities ρA=ρB=1/2ρ_{A}=ρ_{B}=1/2. In addition to the density wave phase reported in the experiment, we find several regimes of superfluidity when one or two hopping parameters are large enough, and interestingly there is a supercounterfluid phase at moderate and comparable hopping parameters. The universality classes of these phase transitions are analyzed from the correlation functions, excitation gaps, and entanglement entropy. In particular, a Berezinskii-Kosterlitz-Thouless type is recognized several gapped-to-gapless transitions. In addition, we also study the quantum phase transitions when varying ρBρ_{B} from 0 to 1 while keeping ρA=1/2ρ_A = 1/2. We identify a supersolid phase in a wide range of 1/2<ρB<11/2<ρ_B<1. Our work paves the way for realizing exotic many-body phases in cold atom experiments upon proper tuning of experimental parameters.

Tensor-based homogeneous polynomial dynamical system analysis from data

Authors: Xin Mao, Anqi Dong, Ziqin He, Yidan Mei, Shenghan Mei, Can Chen

arXiv ID: 2503.17774 | Date: 2025-03-22

Abstract: Numerous complex real-world systems, such as those in biological, ecological, and social networks, exhibit higher-order interactions that are often modeled using polynomial dynamical systems or homogeneous polynomial dynamical systems (HPDSs). However, identifying system parameters and analyzing key system-theoretic properties remain challenging due to their inherent nonlinearity and complexity, particularly for large-scale systems. To address these challenges, we develop an innovative computational framework in this article that leverages advanced tensor decomposition techniques, namely tensor train and hierarchical Tucker decompositions, to facilitate efficient identification and analysis of HPDSs that can be equivalently represented by tensors. Specifically, we introduce memory-efficient system identification techniques for directly estimating system parameters represented through tensor decompositions from time-series data. Additionally, we develop necessary and sufficient conditions for determining controllability and observability using the tensor decomposition-based representations of HPDSs, accompanied by detailed complexity analyses that demonstrate significant reductions in computational demands. The effectiveness and efficiency of our framework are validated through numerical examples.

Solving tiling enumeration problems by tensor network contractions

Authors: Kai Liang

arXiv ID: 2503.17698 | Date: 2025-03-22

Abstract: This paper presents an algorithm for computing the contraction of two-dimensional tensor networks on a square lattice; and we combine it with solving congruence equations to compute the exact enumeration (including weighted enumeration) of Wang tilings. Based on this, the paper demonstrates how to transform other tiling enumeration problems (such as those of polyominoes) into Wang tiling enumeration problems, thereby solving them using this algorithm. Our algorithm extends the sequence length records for dozens of sequences defined by polyomino tiling enumeration on chessboards on the OEIS website, covering numerous of different polyomino sets, including I-polyominoes, tetrominoes, pentominoes, etc. This demonstrates the high efficiency and strong universality of the algorithm for solving exact tiling enumeration problems. In addition, the theory and techniques used in the algorithm establish a bridge between tensor network contractions and tiling enumeration, where the former provides a theoretical foundation for solving problems in the latter, while the latter offers an intuitive combinatorial interpretation of the former.

Tensor Cross Interpolation of Purities in Quantum Many-Body Systems

Authors: Dmytro Kolisnyk, Raimel A. Medina, Romain Vasseur, Maksym Serbyn

arXiv ID: 2503.17230 | Date: 2025-03-21

Abstract: A defining feature of quantum many-body systems is the exponential scaling of the Hilbert space with the number of degrees of freedom. This exponential complexity naïvely renders a complete state characterization, for instance via the complete set of bipartite Renyi entropies for all disjoint regions, a challenging task. Recently, a compact way of storing subregions' purities by encoding them as amplitudes of a fictitious quantum wave function, known as entanglement feature, was proposed. Notably, the entanglement feature can be a simple object even for highly entangled quantum states. However the complexity and practical usage of the entanglement feature for general quantum states has not been explored. In this work, we demonstrate that the entanglement feature can be efficiently learned using only a polynomial amount of samples in the number of degrees of freedom through the so-called tensor cross interpolation (TCI) algorithm, assuming it is expressible as a finite bond dimension MPS. We benchmark this learning process on Haar and random MPS states, confirming analytic expectations. Applying the TCI algorithm to quantum eigenstates of various one dimensional quantum systems, we identify cases where eigenstates have entanglement feature learnable with TCI. We conclude with possible applications of the learned entanglement feature, such as quantifying the distance between different entanglement patterns and finding the optimal one-dimensional ordering of physical indices in a given state, highlighting the potential utility of the proposed purity interpolation method.

Ergodic behaviors in reversible 3-state cellular automata

Authors: Rustem Sharipov, Matija Koterle, Sašo Grozdanov, Tomaž Prosen

arXiv ID: 2503.16593 | Date: 2025-03-20

Abstract: Classical cellular automata represent a class of explicit discrete spacetime lattice models in which complex large-scale phenomena emerge from simple deterministic rules. With the goal to uncover different physically distinct classes of ergodic behavior, we perform a systematic study of three-state cellular automata (with a stable `vacuum' state and `particles' with ±\pm charges). The classification is aided by the automata's different transformation properties under discrete symmetries: charge conjugation, spatial parity and time reversal. In particular, we propose a simple classification that distinguishes between types and levels of ergodic behavior in such system as quantified by the following observables: the mean return time, the number of conserved quantities, and the scaling of correlation functions. In each of the physically distinct classes, we present examples and discuss some of their phenomenology. This includes chaotic or ergodic dynamics, phase-space fragmentation, Ruelle-Pollicott resonances, existence of quasilocal charges, and anomalous transport with a variety of dynamical exponents.

Many exact area-law scar eigenstates in the nonintegrable PXP and related models

Authors: Andrew N. Ivanov, Olexei I. Motrunich

arXiv ID: 2503.16327 | Date: 2025-03-20

Abstract: In this work, we present new, highly non-trivial area-law exact zero-energy eigenstates of the one-dimensional (1D) PXP and related models. We formulate sufficient conditions for a matrix product state to represent an exact zero-energy eigenstate of a given 1D kinetically constrained model and use them to prove our new states. We also demonstrate that all previously known exact eigenstates of PXP-type models satisfy these conditions, and, in fact, can be directly deduced from them. We discuss and demonstrate a remarkably effective general numerical technique for discovering finite-bond-dimension eigenstates residing in degenerate subspaces of a broad class of Hamiltonians. Our results highlight a previously unrecognized structure characteristic of the exponentially large nullspaces in kinetically constrained models, suggesting the possibly of extensively many increasingly complex area-law zero-energy eigenstates in the thermodynamic limit. The important implications of these emergent exact eigenstates for the general thermalization phenomenology are exemplified by one of the states introduced in this work, which we propose is a member of the primary Z2\mathbb{Z}_2 quantum many-body scar tower responsible for long-lived revivals in the Rydberg atom chain experiment.

Skyrmionic Schrödinger cat states in monoaxial chiral magnets

Authors: Stefan Liscak, Andreas Haller, Andreas Michels, Thomas L. Schmidt, Vladyslav M. Kuchkin

arXiv ID: 2503.16020 | Date: 2025-03-20

Abstract: We study the low-energy excitation spectra of a spin-1/2 quantum Heisenberg model with a monoaxial Dzyaloshinskii-Moriya interaction. Using the density matrix renormalization group method, our analysis reveals a degeneracy between skyrmion and antiskyrmion states, enabling the formation of a mesoscopic Schrödinger cat state - a quantum superposition of these topologically distinct textures. To characterize this nontrivial state, we compute two-point spin correlation functions, highlighting signatures accessible via neutron scattering experiments. Furthermore, we demonstrate that applying a magnetic field gradient induces a coherent time evolution of the cat state, offering a controllable mechanism for its manipulation. These findings provide a framework for the detection of skyrmionic Schrödinger cat states in quantum magnets.

Reducing T Gates with Unitary Synthesis

Authors: Tianyi Hao, Amanda Xu, Swamit Tannu

arXiv ID: 2503.15843 | Date: 2025-03-20

Abstract: Quantum error correction is essential for achieving practical quantum computing but has a significant computational overhead. Among fault-tolerant (FT) gate operations, non-Clifford gates, such as TT, are particularly expensive due to their reliance on magic state distillation. These costly TT gates appear frequently in FT circuits as many quantum algorithms require arbitrary single-qubit rotations, such as RxR_x and RzR_z gates, which must be decomposed into a sequence of TT and Clifford gates. In many quantum circuits, RxR_x and RzR_z gates can be fused to form a single U3U3 unitary. However, existing synthesis methods, such as gridsynth, rely on indirect decompositions, requiring separate RzR_z decompositions that result in a threefold increase in TT count. This work presents a novel FT synthesis algorithm that directly synthesizes arbitrary single-qubit unitaries, avoiding the overhead of separate RzR_z decompositions. By leveraging tensor network-based search, our approach enables native U3U3 synthesis, reducing the TT count, Clifford gate count, and approximation error. Compared to gridsynth-based circuit synthesis, for 187 representative benchmarks, our design reduces the TT count by up to 3.5×3.5\times, and Clifford gates by 7×7\times, resulting in up to 4×4\times improvement in overall circuit infidelity.

Rapid quantum ground state preparation via dissipative dynamics

Authors: Yongtao Zhan, Zhiyan Ding, Jakob Huhn, Johnnie Gray, John Preskill, Garnet Kin-Lic Chan, Lin Lin

arXiv ID: 2503.15827 | Date: 2025-03-20

Abstract: Inspired by natural cooling processes, dissipation has become a promising approach for preparing low-energy states of quantum systems. However, the potential of dissipative protocols remains unclear beyond certain commuting Hamiltonians. This work provides significant analytical and numerical insights into the power of dissipation for preparing the ground state of non-commuting Hamiltonians. For quasi-free dissipative dynamics, including certain 1D spin systems with boundary dissipation, our results reveal a new connection between the mixing time in trace distance and the spectral properties of a non-Hermitian Hamiltonian, leading to an explicit and sharp bound on the mixing time that scales polynomially with system size. For more general spin systems, we develop a tensor network-based algorithm for constructing the Lindblad jump operator and for simulating the dynamics. Using this algorithm, we demonstrate numerically that dissipative ground state preparation protocols can achieve rapid mixing for certain 1D local Hamiltonians under bulk dissipation, with a mixing time that scales logarithmically with the system size. We then prove the rapid mixing result for certain weakly interacting spin and fermionic systems in arbitrary dimensions, extending recent results for high-temperature quantum Gibbs samplers to the zero-temperature regime. Our theoretical approaches are applicable to systems with singular stationary states, and are thus expected to have applications beyond the specific systems considered in this study.

Absolutely Maximal Entanglement in Continuous Variables

Authors: James I. Kwon, Anthony J. Brady, Victor V. Albert

arXiv ID: 2503.15698 | Date: 2025-03-19

Abstract: We explore absolutely maximal entanglement (AME) and k-uniformity in continuous-variable (CV) quantum systems, and show that-unlike in qudit systems-such entanglement is readily realizable in both Gaussian and non-Gaussian quantum states of multiple modes. We demonstrate that Gaussian CV cluster states are generically AME, rederiving the results of [Phys. Rev. Lett. 103, 070501 (2009)] from a generalized stabilizer formalism, and provide explicit constructions based on Cauchy, Vandermonde, totally positive, and real-block-code generator matrices. We further extend AME properties to a family of non-Gaussian states constructed from discrete Zak basis states that incorporate grid states (a.k.a., Gottesman-Kitaev-Preskill states) as non-Gaussian resources. Realizations of CV AME states enable open-destination multi-party CV teleportation, CV quantum secret sharing, CV majority-agreed key distribution, perfect-tensor networks on arbitrary geometries, and multi-unitary circuits. Our extension to non-Gaussian AME states may further provide robustness to Gaussian noise and benefits to quantum CV information processing.

pyTTN: An Open Source Toolbox for Open and Closed System Quantum Dynamics Simulations Using Tree Tensor Networks

Authors: Lachlan P Lindoy, Daniel Rodrigo-Albert, Yannic Rath, Ivan Rungger

arXiv ID: 2503.15460 | Date: 2025-03-19

Abstract: We present the Python Tree Tensor Network package (pyTTN) for the evaluation of dynamical properties of closed and open quantum systems that makes use of Tree Tensor Network (TTN), or equivalently the multi-layer multiconfiguration time-dependent Hartree (ML-MCTDH), based representations of wavefunctions. This package includes several features allowing for easy setup of zero- and finite-temperature calculations for general Hamiltonians using single and multi-set TTN ansätze with an adaptive bond dimension through the use of subspace expansion techniques. All core features are implemented in C++ with Python bindings provided to simplify the use of this package. In addition to these core features, pyTTN provides several tools for setting up efficient simulation of open quantum system dynamics, including the use of the TTN ansatz to represent the auxiliary density operator space for the simulation of the Hierarchical Equation of Motion (HEOM) method and generalised pseudomode methods; furthermore we demonstrate that the two approaches are equivalent up to a non-unitary normal mode transformation acting on the pseudomode degrees of freedom. We present a set of applications of the package, starting with the widely used benchmark case of the photo-excitation dynamics of 24 mode pyrazine, following which we consider a more challenging model describing the exciton dynamics at the interface of a nn-oligothiophene donor-C60_{60} fullerene acceptor system. Finally, we consider applications to open quantum systems, including the spin-boson model, a set of extended dissipative spin models, and an Anderson impurity model. By combining ease of use, an efficient implementation, as well as an extendable design allowing for the addition of future extensions, pyTTN can be integrated in a wide range of computational modelling software.

Nonequilibrium Statistics of Biased Kondo Resonance

Authors: Jong E. Han

arXiv ID: 2503.14400 | Date: 2025-03-18

Abstract: Numerical renormalization group (NRG) is formulated for nonequilibrium steady-state by converting finite-lattice many-body eigenstates into scattering states. Extension of the full-density-matrix NRG for a biased Anderson impurity model, simplified by formulating with the original orbital basis as the Hamiltonian, enables detailed studies of the sub-Kondo spectral evolution in the zero-temperature limit, confirming the double-resonance structure at bias of the Kondo energy scale TKT_K. The distribution shows distinct multi-scale spectral features at energy ωω below the Kondo scale (ωTKω\lesssim T_K) and near the bias (ωVω\gtrsim V), leading to the nonequilibrium temperature TlocT_{\rm loc} local to the Kondo dot scaling as kBTlocVk_BT_{\rm loc}\approx V for VTKV\gg T_K. The current-voltage relation in the low-temperature limit (TTKT\ll T_K) deviates from the unitary limit as the bias exceeds the Kondo scale (V/2TKV/2\gtrsim T_K) and reaches the current saturation regime.

Quantum Strong-to-Weak Spontaneous Symmetry Breaking in Decohered One Dimensional Critical States

Authors: Yuxuan Guo, Sheng Yang, Xue-Jia Yu

arXiv ID: 2503.14221 | Date: 2025-03-18

Abstract: Symmetry breaking has been a central theme in classifying quantum phases and phase transitions. Recently, this concept has been extended to the mixed states of open systems, attracting considerable attention due to the emergence of novel physics beyond closed systems. In this work, we reveal a new type of phase transition in mixed states, termed \emph{quantum} strong-to-weak spontaneous symmetry breaking (SWSSB). Using a combination of field theory calculations and large-scale matrix product state simulations, we map out the global phase diagram of the XXZ critical spin chain under local strong symmetry preserving decoherence, which features an SWSSB phase and a trivial Luttinger liquid phase, separated by a straight critical line that belongs to the boundary Berezinskii-Kosterlitz-Thouless universality class with a varying effective central charge. Importantly, we analyze this transition from two complementary perspectives: on one hand, through the behavior of order parameters that characterize the symmetry breaking; on the other hand, from a quantum information viewpoint by studying entropic quantities and the concept of quantum recoverability. Remarkably, the SWSSB transition in our case is \emph{purely quantum} in the sense that it can only be driven by tuning the Hamiltonian parameter even under arbitrary decoherence strength, fundamentally distinguishing it from the decoherence-driven SWSSB transitions extensively discussed in previous literature. Importantly, our unified theoretical framework is applicable to a broad class of one-dimensional quantum systems, including spin chains and fermionic systems, whose low-energy physics can be described by Luttinger liquid theory, under arbitrary symmetry-preserving decoherence channels. Finally, we also discuss the experimental relevance of our theory on quantum simulator platforms.

Ace-TN: GPU-Accelerated Corner-Transfer-Matrix Renormalization of Infinite Projected Entangled-Pair States

Authors: Addison D. S. Richards, Erik S. Sørensen

arXiv ID: 2503.13900 | Date: 2025-03-18

Abstract: The infinite projected entangled-pair state (iPEPS) ansatz is a powerful tensor-network approximation of an infinite two-dimensional quantum many-body state. Tensor-based calculations are particularly well-suited to utilize the high parallel efficiency of modern GPUs. We present Ace-TN, a modular and easily extendable open-source library developed to address the current need for an iPEPS framework focused on GPU acceleration. We demonstrate the advantage of using GPUs for the core iPEPS simulation methods and present a simple parallelization scheme for efficient multi-GPU execution. The latest distribution of Ace-TN can be obtained at https://github.com/ace-tn/ace-tn.

Resolving space-time structures of quantum impurities with a numerically exact few-body algorithm

Authors: Yuriel Núñez-Fernández, Maxime Debertolis, Serge Florens

arXiv ID: 2503.13706 | Date: 2025-03-17

Abstract: We introduce a numerically exact real-time evolution scheme for quantum impurities in a macroscopically large bath. The algorithm is few-body revealing, namely it identifies the electronic orbitals that can be made inactive (in a trivial product state) by a time-dependent orbital rotation. Following a quench, we show that both the number of active orbitals and their associated matrix product state bond dimensions saturate to small values, leading to an algorithm dramatically more accurate and faster than the state of the art. We are thus able to follow the dynamics for thousands of fermions, up to the long-time stationary regime, and to study subtle aspects of quantum relaxation in the spatio-temporal domain, such as the emergence of entanglement structures in the Kondo screening cloud.

Interpolation categories for Conformal Embeddings

Authors: Cain Edie-Michell, Noah Snyder

arXiv ID: 2503.13641 | Date: 2025-03-17

Abstract: In this paper we give a diagrammatic description of the categories of modules coming from the conformal embeddings V(slN,N)V(soN21,1)\mathcal{V}(\mathfrak{sl}_N,N) \subset \mathcal{V}(\mathfrak{so}_{N^2-1},1). A small variant on this construction (morally corresponding to a conformal embedding of glN\mathfrak{gl}_N level NN into oN21\mathfrak{o}_{N^2-1} level 11) has uniform generators and relations which are rational functions in q=e2πi/4Nq = e^{2 πi/4N}, which allows us to construct a new continuous family of tensor categories at non-integer level which interpolate between these categories. This is the second example of such an interpolation category for families of conformal embeddings after Zhengwei Liu's interpolation categories V(slN,N±2)V(slN(N±1)/2,1)\mathcal{V}(\mathfrak{sl}_N, N\pm 2) \subset \mathcal{V}(\mathfrak{sl}_{N(N\pm 1)/2},1) which he constructed using his classification Yang-Baxter planar algebras. Our approach is different from Liu's, we build a two-color skein theory, with one strand coming from XX the image of defining representation of slN\mathfrak{sl}_N and the other strand coming from an invertible object gg in the category of local modules, and a trivalent vertex coming from a map XXgX \otimes X^* \rightarrow g. We anticipate small variations on our approach will yield interpolation categories for every infinite discrete family of conformal embeddings.

Stabilizer Rényi Entropy and Conformal Field Theory

Authors: Masahiro Hoshino, Masaki Oshikawa, Yuto Ashida

arXiv ID: 2503.13599 | Date: 2025-03-17

Abstract: Understanding universal aspects of many-body systems is one of the central themes in modern physics. Recently, the stabilizer Rényi entropy (SRE) has emerged as a computationally tractable measure of nonstabilizerness, a crucial resource for fault-tolerant universal quantum computation. While numerical results suggested that the SRE in critical states can exhibit universal behavior, its comprehensive theoretical understanding has remained elusive. In this work, we develop a field-theoretical framework for the SRE in a (1+1)(1+1)-dimensional many-body system and elucidate its universal aspects using boundary conformal field theory. We demonstrate that the SRE is equivalent to a participation entropy in the Bell basis of a doubled Hilbert space, which can be calculated from the partition function of a replicated field theory with the interlayer line defect created by the Bell-state measurements. This identification allows us to characterize the universal contributions to the SRE on the basis of the data of conformal boundary conditions imposed on the replicated theory. We find that the SRE of the entire system contains a universal size-independent term determined by the noninteger ground-state degeneracy known as the g-factor. In contrast, we show that the mutual SRE exhibits the logarithmic scaling with a universal coefficient given by the scaling dimension of a boundary condition changing operator, which elucidates the origin of universality previously observed in numerical results. As a concrete demonstration, we present a detailed analysis of the Ising criticality, where we analytically derive the universal quantities at arbitrary Rényi indices and numerically validate them with high accuracy by employing tensor network methods. These results establish a field-theoretical approach to understanding the universal features of nonstabilizerness in quantum many-body systems.

Quantum-Enhanced LLM Efficient Fine Tuning

Authors: Xiaofei Kong, Lei Li, Zhaoyun Chen, Cheng Xue, Xiaofan Xu, Huanyu Liu, Yuchun Wu, Yuan Fang, Han Fang, Kejiang Chen, Yang Yang, Menghan Dou, Guoping Guo

arXiv ID: 2503.12790 | Date: 2025-03-17

Abstract: Low-Rank Adaptation (LoRA) enables efficient fine-tuning of pre-trained language models through low-rank matrix approximation, achieving effectiveness in many scenarios. However, its representation capacity is constrained in complex tasks or high-rank dependency settings, potentially limiting model adaptability. To overcome the expressive bottleneck in classical low-rank approximation for fine-tuning large language models (LLMs), we propose Quantum Tensor Hybrid Adaptation (QTHA), a parameter-efficient fine-tuning method that integrates a quantum neural network (QNN) with a tensor network. QTHA explores quantum tensor hybrid fine-tuning within low-rank spaces by decomposing pre-trained weights into quantum neural network and tensor network representations, leveraging quantum state superposition to overcome classical rank limitations. Experiments demonstrate that QTHA achieves performance comparable to or surpassing LoRA in parameter-efficient fine-tuning. Compared to LoRA, QTHA reduces trainable parameters by 76% while reducing training loss by up to 17% and improving test set performance by up to 17% within the same training steps. This research not only enables lightweight adaptation of quantum resources to the billion-parameter models but also validates the feasibility of quantum hardware optimization driven by LLM tasks. It establishes the first engineering-ready foundation for future quantum-enhanced Artificial General Intelligence (AGI) systems.

Boundary Conditions for the Entanglement Cut in 2D Conformal Field Theories

Authors: Ananda Roy, Sergei L. Lukyanov, Hubert Saleur

arXiv ID: 2503.12674 | Date: 2025-03-16

Abstract: The entanglement spectra for a subsystem in a spin chain fine-tuned to a quantum-critical point contains signatures of the underlying quantum field theory that governs its low-energy properties. For an open chain with given boundary conditions described by a 2D conformal field theory~(CFT), the entanglement spectrum of the left/right half of the system coincides with a boundary CFT spectrum, where one of the boundary conditions arise due to the `entanglement cut'. The latter has been argued to be conformal and has been numerically found to be the `free' boundary condition for Ising, Potts and free boson theories. For these models, the `free' boundary condition for the lattice degree of freedom has a counterpart in the continuum theory. However, this is not true in general. Here, this question is analyzed for the unitary minimal models of 2D CFTs using the density matrix renormalization group technique. The entanglement spectra are computed for blocks of spins in open chains of A-type restricted solid-on-solid models with identical boundary conditions at the ends. The imposed boundary conditions are realized exactly for these lattice models due to their integrable nature. The obtained entanglement spectra are in good agreement with certain boundary CFT spectra. The boundary condition for the entanglement cut is found to be conformal and to coincide with the one with the highest boundary entropy. This identification enables determination of the exponents governing the unusual corrections to the entanglement entropy from the CFT partition functions. These are compared with numerical results.

Non-equilibrium origin of cavity-induced resonant modifications of chemical reactivities

Authors: Yaling Ke

arXiv ID: 2503.12568 | Date: 2025-03-16

Abstract: In this work, we investigate the influence of light-matter coupling on reaction dynamics and equilibrium properties of a single molecule inside an optical cavity. The reactive molecule is modeled using a triple-well potential, allowing two competing reaction pathways that yield distinct products. Dynamical and equilibrium simulations are performed using the numerically exact hierarchical equations of motion approach in real- and imaginary-time formulations, respectively, both implemented with tree tensor network decomposition schemes. We consider two illustrative cases: one dominated by slow kinetics and another by ultrafast processes. Our results demonstrate that the rates of ground-state reaction pathways can be selectively enhanced when the cavity frequency is tuned into resonance with a vibrational transition directly leading to the formation of the corresponding product, even when that transition is spectroscopically dark. However, tuning cavity frequency to match an absorption-dominant transition shared across both reaction pathways does not necessarily result in pronounced rate enhancements and selectivity. Together with an additional analysis using an asymmetric double-well model, we highlight the greater complexity of underlying factors governing chemical reactivity, which extend beyond considerations of transition dipole strengths and thermal population distributions that shape linear spectroscopy. Furthermore, we found that in all scenarios, the equilibrium populations remain unchanged when the molecule is moved into the cavity, regardless of the cavity frequency. Thus, our study confirms at a fully quantum-mechanical level that cavity-induced modifications of chemical reactivities in resonant conditions arise from dynamical and non-equilibrium interactions between the cavity mode and molecular vibrations, rather than from the significant changes in equilibrium properties.

Emergent quasi-particles of spin-1 trimer chain

Authors: Manodip Routh, Anutosh Biswas, Manoranjan Kumar

arXiv ID: 2503.12565 | Date: 2025-03-16

Abstract: The recent experimental realization of emergent quasi-particles, such as spinons, doublons, and quartons, in a spin-1/21/2 trimer chain has spurred new interest in low dimensional magnetic systems. In this study, we investigate the dynamical properties of the isotropic spin-11 trimer chain with intra and inter-trimer antiferromagnetic exchange couplings, (J>0J >0 and J>0J' >0), respectively, unveiling various quasi-particles: magnons, singletons, triplons, pentons, and heptons. For weak inter-trimer exchange coupling J/J1J'/J \ll 1, it behaves as an effective spin-11 chain with valence bond solid (VBS) ground state. Employing density matrix renormalization group (DMRG) techniques, we compute the dynamic structure factor (DSF) which reveals a gapped magnon band alongside weakly dispersive singleton, excited triplon, and penton excitations. The evolution of these excitations with inter-trimer coupling JJ' is also examined, providing insight into the underlying excitation mechanisms. For spin-11 chain, these exotic quasi-particles eventually reduce to conventional magnon excitations as J/J1J'/J \rightarrow 1. Our results shed light on the rich and complex excitation spectrum of spin-11 trimer chains and offer unique perspectives on the dynamics in quantum spin systems.

Efficient optimization and conceptual barriers in variational finite Projected Entangled-Pair States

Authors: Daniel Alcalde Puente, Erik Lennart Weerda, Konrad Schröder, Matteo Rizzi

arXiv ID: 2503.12557 | Date: 2025-03-16

Abstract: Projected entangled pair states (PEPS) on finite two-dimensional lattices are a natural ansatz for representing ground states of local many-body Hamiltonians, as they inherently satisfy the boundary law of entanglement entropy. In this paper, we propose the optimization of PEPS via an improved formulation of the time-dependent variational principle (TDVP), namely the minimum-step stochastic-reconfguration scheme recently introduced for neural quantum states. We further discuss possible numerical issues that might arise in such a sampling-based approach. In this context, investigate the entanglement properties of random PEPS and find an entanglement phase transition. We note that on one side of this transition, we can identify positive random tensors as product states. To demonstrate the power of the framework described in this paper, we apply the PEPS to study the notoriously challenging chiral spin liquids. Moreover, we exhibit our approach's capability to naturally handle long-range interactions by exploring the phase diagram of Rydberg atom arrays with long-range interactions. We further provide parallelized easy-to-use code, allowing the straightforward application of our method to general Hamiltonians composed of local interaction terms.

A Bond weighted tensor renormalization group study of the q-state ferromagnetic Potts models on the square lattice

Authors: Yuan-Heng Tseng, Shang-Wei Li, Fu-Jiun Jiang

arXiv ID: 2503.12361 | Date: 2025-03-16

Abstract: It is known rigorously that the phase transition of the qq-state ferromagnetic Potts model on the square lattice is second order for q=4q=4. Despite this fact, some observables of the q=4q=4 model show features of a first-order phase transition. For example, negative peak appears for the quantity of Binder ratio Q2Q_2 of this model. Such a non-monotonic behavior of Q2Q_2 is typically a consequence of phase coexistence, hence is served as a signal of a first-order phase transition. In particular, the negative peak should diverge with linear system size LL squared. Since the mentioned divergence phenomenon is not observed for the 4-state Potts model, the scenario of a first-order phase transition for this model is ruled out. Interestingly, a recent large scale Monte Carlo investigation of the 4-state Potts model observes that the two-peak structure of the energy density distribution becomes more noticeable when LL increases. This finding indicates the signal of coexistence of phases is getting stronger with LL. Due to these unusual critical behaviors, here we study the energy density EE and the specific heat CvC_v of the 4-state Potts model on the square lattice using the technique of bond weighted tensor renormalization group (BWTRG). For a comparison purpose, q=2q=2 and q=5q=5 ferromagnetic Potts models on the square lattice are investigated using the same method as well. Remarkably, our results do imply there may be a small energy gap for q=4q=4 model. While the appearance of the mentioned small energy gap can be explained plausibly and it will disappear with a more sophisticated investigation, our finding suggests that whether a message of a first-order phase transition is genuine or is an artificial effect requires further and detailed investigations.

Circuit Design based on Feature Similarity for Quantum Generative Modeling

Authors: Mathis Makarski, Jumpei Kato, Yuki Sato, Naoki Yamamoto

arXiv ID: 2503.11983 | Date: 2025-03-15

Abstract: Quantum generative models may achieve an advantage on quantum devices by their inherent probabilistic nature and efficient sampling strategies. However, current approaches mostly rely on general-purpose circuits, such as the hardware efficient ansatz paired with a random initialization strategy, which are known to suffer from trainability issues such as barren plateaus. To address these issues, a tensor network pretraining framework that initializes a quantum circuit ansatz with a classically computed high-quality solution for a linear entanglement structure has been proposed in literature. In order to improve the classical solution, the quantum circuit needs to be extended, while it is still an open question how the extension affects trainability. In this work, we propose the metric-based extension heuristic to design an extended circuit based on a similarity metric measured between the dataset features. We validate this method on the bars and stripes dataset and carry out experiments on financial data. Our results underline the importance of problem-informed circuit design and show that the metric-based extension heuristic offers the means to introduce inductive bias while designing a circuit under limited resources.

Thermodynamics of the Hubbard Model on the Bethe Lattice

Authors: Jia-Lin Chen, Zhen Fan, Bo Zhan, Jiahang Hu, Tong Liu, Junyi Ji, Kang Wang, Hai-Jun Liao, Tao Xiang

arXiv ID: 2503.11598 | Date: 2025-03-14

Abstract: We investigate the thermodynamic properties of the Hubbard model on the Bethe lattice with a coordination number of 3 using the thermal canonical tree tensor network method. Our findings reveal two distinct thermodynamic phases: a low-temperature antiferromagnetic phase, where spin SU(2) symmetry is broken, and a high-temperature paramagnetic phase. A key feature of the system is the separation of energy scales for charge and spin excitations, which is reflected in the temperature dependence of thermodynamic quantities and the disparity between spin and charge gaps extracted from their respective susceptibilities. At the critical point, both spin and charge susceptibilities exhibit singularities, suggesting that charge excitations are not fully decoupled from their spin counterparts. Additionally, the double occupancy number exhibits a non-monotonic temperature dependence, indicative of an entropy-driven Pomeranchuk effect. These results demonstrate that the loopless Bethe lattice effectively captures the essential physics of the Hubbard model while providing a computationally efficient framework for studying strongly correlated electronic systems.

Deconfined quantum criticality in a frustrated Haldane chain with single-ion anisotropy

Authors: Niels T. Pronk, Bowy M. La Rivière, Natalia Chepiga

arXiv ID: 2503.11413 | Date: 2025-03-14

Abstract: We report a phase diagram of the antiferromagnetic spin-1 chain with nearest-neighbor Heisenberg and three-site interactions in the presence of single-ion anisotropy. We show that the Gaussian and Ising transitions that separate the topological Haldane phase from the two anisotropic phases eventually fuse into a higher symmetry point characterized by the Wess-Zumino-Witten (WZW) SU(2)2_2 critical theory providing a lattice realization of the conformal embedding. On the other side of the WZW multi-critical point, the Ising critical line reappears together with the eight-vertex transition. This transition is a one-dimensional realization of a deconfined quantum criticality separating the dimerized and Ising antiferromagnetic phases - two ordered phases with incompatible order parameters.

Wavefunction optimization at the complete basis set limit with Multiwavelets and DMRG

Authors: Martina Nibbi, Luca Frediani, Evgueni Dinvay, Christian B. Mendl

arXiv ID: 2503.10808 | Date: 2025-03-13

Abstract: The density matrix renormalization group (DMRG) is a powerful numerical technique to solve strongly correlated quantum systems: it deals well with systems which are not dominated by a single configuration (unlike Coupled Cluster) and it converges rapidly to the Full Configuration Interaction (FCI) limit (unlike truncated Configuration Interaction (CI) expansions). In this work, we develop an algorithm integrating DMRG within the multiwavelet-based multiresolution analysis (MRA). Unlike fixed basis sets, multiwavelets offer an adaptive and hierarchical representation of functions, approaching the complete basis set limit to a specified precision. As a result, this combined technique leverages the multireference capability of DMRG and the complete basis set limit of MRA and multiwavelets. More specifically, we adopt a pre-existing Lagrangian optimization algorithm for orbitals represented in the MRA domain and improve its computational efficiency by replacing the original CI calculations with DMRG. Additionally, we substitute the reduced density matrices computation with the direct extraction of energy gradients from the DMRG tensors. We apply our method to small systems such H2, He, HeH2, BeH2 and N2. The results demonstrate that our approach reduces the final energy while keeping the number of orbitals low compared to FCI calculations on an atomic orbital basis set.

Simple Hamiltonians for Matrix Product State models

Authors: Norbert Schuch, Andras Molnar, David Perez-Garcia

arXiv ID: 2503.10767 | Date: 2025-03-13

Abstract: Matrix Product States (MPS) and Tensor Networks provide a general framework for the construction of solvable models. The best-known example is the Affleck-Kennedy-Lieb-Tasaki (AKLT) model, which is the ground state of a 2-body nearest-neighbor parent Hamiltonian. We show that such simple parent Hamiltonians for MPS models are, in fact, much more prevalent than hitherto known: The existence of a single example with a simple Hamiltonian for a given choice of dimensions already implies that any generic MPS with those dimensions possesses an equally simple Hamiltonian. We illustrate our finding by discussing a number of models with nearest-neighbor parent Hamiltonians, which generalize the AKLT model on various levels.

Quantum complexity in gravity, quantum field theory, and quantum information science

Authors: Stefano Baiguera, Vijay Balasubramanian, Pawel Caputa, Shira Chapman, Jonas Haferkamp, Michal P. Heller, Nicole Yunger Halpern

arXiv ID: 2503.10753 | Date: 2025-03-13

Abstract: Quantum complexity quantifies the difficulty of preparing a state or implementing a unitary transformation with limited resources. Applications range from quantum computation to condensed matter physics and quantum gravity. We seek to bridge the approaches of these fields, which define and study complexity using different frameworks and tools. We describe several definitions of complexity, along with their key properties. In quantum information theory, we focus on complexity growth in random quantum circuits. In quantum many-body systems and quantum field theory (QFT), we discuss a geometric definition of complexity in terms of geodesics on the unitary group. In dynamical systems, we explore a definition of complexity in terms of state or operator spreading, as well as concepts from tensor-networks. We also outline applications to simple quantum systems, quantum many-body models, and QFTs including conformal field theories (CFTs). Finally, we explain the proposed relationship between complexity and gravitational observables within the holographic anti-de Sitter (AdS)/CFT correspondence.

Grokking as an entanglement transition in tensor network machine learning

Authors: Domenico Pomarico, Alfonso Monaco, Giuseppe Magnifico, Antonio Lacalamita, Ester Pantaleo, Loredana Bellantuono, Sabina Tangaro, Tommaso Maggipinto, Marianna La Rocca, Ernesto Picardi, Nicola Amoroso, Graziano Pesole, Sebastiano Stramaglia, Roberto Bellotti

arXiv ID: 2503.10483 | Date: 2025-03-13

Abstract: Grokking is a intriguing phenomenon in machine learning where a neural network, after many training iterations with negligible improvement in generalization, suddenly achieves high accuracy on unseen data. By working in the quantum-inspired machine learning framework based on tensor networks, we numerically prove that grokking phenomenon can be related to an entanglement dynamical transition in the underlying quantum many-body systems, consisting in a one-dimensional lattice with each site hosting a qubit. Two datasets are considered as use case scenarios, namely fashion MNIST and gene expression communities of hepatocellular carcinoma. In both cases, we train Matrix Product State (MPS) to perform binary classification tasks, and we analyse the learning dynamics. We exploit measurement of qubits magnetization and correlation functions in the MPS network as a tool to identify meaningful and relevant gene subcommunities, verified by means of enrichment procedures.

Towards Using Matrix-Free Tensor Decompositions to Systematically Improve Approximate Tensor-Networks

Authors: Karl Pierce

arXiv ID: 2503.10380 | Date: 2025-03-13

Abstract: We investigate a novel approach to approximate tensor-network contraction via the exact, matrix-free decomposition of full tensor-networks. We study this method as a means to eliminate the propagation of error in the approximation of tensor-networks. Importantly, this decomposition-based approach is generic, i.e. it does not depend on a specific tensor-network, the tensor index (physical) ordering, or the choice of tensor decomposition. Careful consideration should be made to determine the best decomposition strategy. Furthermore, this method does not rely on robust cancellation of errors (i.e. the Taylor expansion). As a means to study the effectiveness of the approach, we replace the exact contraction of the particle particle ladder (PPL) tensor diagram in the popular coupled-cluster with single and double excitation (CCSD) method with a low-rank tensor decomposition, namely the canonical polyadic decomposition (CPD). With this approach, we replace an O(N6)\mathcal{O}(N^6) tensor contractions with a potentially reduced-scaling O(N4R)\mathcal{O}(N^4R) optimization problem, where RR is the CP rank, and we reduce the computational storage of the PPL tensor from O(N4)\mathcal{O}(N^4) to O(NR)\mathcal{O}(NR), although we do not take advantage of this compression in this study. To minimize the cost of the CPD optimization, we utilize the iterative structure of CCSD to efficiently initialize the CPD optimization. We show that accurate chemically-relevant energy values can be computed with an error of less than 1 kcal/mol using a relatively low CP rank.

Approximation Methods for Simulation and Equivalence Checking of Noisy Quantum Circuits

Authors: Mingyu Huang, Ji Guan, Wang Fang, Mingsheng Ying

arXiv ID: 2503.10340 | Date: 2025-03-13

Abstract: In the current NISQ (Noisy Intermediate-Scale Quantum) era, simulating and verifying noisy quantum circuits is crucial but faces challenges such as quantum state explosion and complex noise representations, constraining simulation and equivalence checking to circuits with a limited number of qubits. This paper introduces an approximation algorithm for simulating and assessing the equivalence of noisy quantum circuits, specifically designed to improve scalability under low-noise conditions. The approach utilizes a novel tensor network diagram combined with singular value decomposition to approximate the tensors of quantum noises. The implementation is based on Google's TensorNetwork Python package for contraction. Experimental results on realistic quantum circuits with realistic hardware noise models indicate that our algorithm can simulate and check the equivalence of QAOA (Quantum Approximate Optimization Algorithm) circuits with around 200 qubits and 20 noise operators, outperforming state-of-the-art approaches in scalability and speed.

Strong-to-weak spontaneous symmetry breaking and average symmetry protected topological order in the doubled Hilbert space

Authors: Yoshihito Kuno, Takahiro Orito, Ikuo Ichinose

arXiv ID: 2503.10311 | Date: 2025-03-13

Abstract: Discovering and categorizing quantum orders in mixed many-body systems are currently one of the most important problems. Target model in this study is an extended version of the cluster model in one dimension with Z2Z2Z_2\otimes Z_2 symmetry, and we investigate effects of decoherence applied to the ground state of the model, focusing on the symmetry aspect. By using a scheme that we propose, a strong symmetry protected topological (SPT) mixed state and double average SPT (ASPT) state are constructed through the pure gapless SPT order and the domain-wall duality. Among them, the double ASPT is categorized by coexisting orders, i.e., a strong-to-weak spontaneous symmetry breaking and ASPT defined by the remaining weak and strong symmetries. We make use of the doubled Hilbert space formalism for the construction scheme. We numerically demonstrate the emergence of the two mixed SPT states and find that a phase transition occurs between them tuned by the strength of decoherence. Finally, we discuss the coexistence of SPT and SWSSB in the double SPT state from the view point of symmetrically invertible property, and comment on the classification of ASPT proposed recently. Suitable multiple-decoherence channel applied to SPT states gives a broad possibility to induce rich ASPTs, possessing non-trivial internal entanglement properties from the view of doubled Hilbert space formalism.

Mixed-state learnability transitions in monitored noisy quantum dynamics

Authors: Hansveer Singh, Romain Vasseur, Andrew C. Potter, Sarang Gopalakrishnan

arXiv ID: 2503.10308 | Date: 2025-03-13

Abstract: We consider learnability transitions in monitored quantum systems that undergo noisy evolution, subject to a global strong symmetry -- i.e., in addition to the measuring apparatus, the system can interact with an unobserved environment, but does not exchange charge with it. As in the pure-state setting, we find two information-theoretic phases -- a sharp (fuzzy) phase in which an eavesdropper can rapidly (slowly) learn the symmetry charge. However, because the dynamics is noisy, both phases can be simulated efficiently using tensor networks. Indeed, even when the true dynamics is unitary, introducing noise by hand allows an eavesdropper to efficiently learn the symmetry charge from local measurements, as we demonstrate. We identify the fuzzy phase in this setting as a mixed-state phase that exhibits spontaneous strong-to-weak symmetry breaking.

New perspectives on Density-Matrix Embedding Theory

Authors: Alicia Negre, Fabian Faulstich, Raehyun Kim, Thomas Ayral, Lin Lin, Eric Cancès

arXiv ID: 2503.09881 | Date: 2025-03-12

Abstract: Quantum embedding methods enable the study of large, strongly correlated quantum systems by (usually self-consistent) decomposition into computationally manageable subproblems, in the spirit of divide-and-conquer methods. Among these, Density Matrix Embedding Theory (DMET) is an efficient approach that enforces self-consistency at the level of one-particle reduced density matrices (1-RDMs), facilitating applications across diverse quantum systems. However, conventional DMET is constrained by the requirement that the global 1-RDM (low-level descriptor) be an orthogonal projector, limiting flexibility in bath construction and potentially impeding accuracy in strongly correlated regimes. In this work, we introduce a generalized DMET framework in which the low-level descriptor can be an arbitrary 1-RDM and the bath construction is based on optimizing a quantitative criterion related to the maximal disentanglement between different fragments. This yields an alternative yet controllable bath space construction for generic 1-RDMs, lifting a key limitation of conventional DMET. We demonstrate its consistency with conventional DMET in appropriate limits and exploring its implications for bath construction, downfolding (impurity Hamiltonian construction), low-level solvers, and adaptive fragmentation. We expect that this more flexible framework, which leads to several new variants of DMET, can improve the robustness and accuracy of DMET.

Fluctuation corrections to the free energy of strongly correlated electron systems

Authors: David Riegler, Jannis Seufert, Ronny Thomale, Peter Wölfle

arXiv ID: 2503.09696 | Date: 2025-03-12

Abstract: We determine the free energy of strongly correlated electron systems in the example of the Hubbard model by calculating the contribution of spin and charge fluctuations to the Gutzwiller approximation mean field result. We employ the slave boson formulation of Kotliar and Ruckenstein in its spin-rotation invariant form in the usual continuous time approximation of the functional integral representation, corrected by "high frequency contributions" (SRIKR+). Previous method-related shortcomings are shown to be overcome when the correct operator ordering for the renormalized kinetic energy is used. The results for the ground state energy in the paramagnetic phase are in very good agreement with state-of-the-art results obtained by methods such as density matrix embedded theory (DMET), quantum Monte Carlo (QMC) and others. The leading low temperature behavior of the free energy allows to extract the quasiparticle effective mass, in particular its enhancement near a continuous phase transition into an ordered state. Our work demonstrates that the SRIKR+ method is competitive with the best available alternative methods and equips the slave-boson approach with an improved synoptic power to explore strongly correlated electron systems.

Variational preparation of normal matrix product states on quantum computers

Authors: Ben Jaderberg, George Pennington, Kate V. Marshall, Lewis W. Anderson, Abhishek Agarwal, Lachlan P. Lindoy, Ivan Rungger, Stefano Mensa, Jason Crain

arXiv ID: 2503.09683 | Date: 2025-03-12

Abstract: Preparing matrix product states (MPSs) on quantum computers is an essential routine in the simulation of many-body physics. However, widely-used schemes based on staircase circuits are often too deep to execute on current hardware. Here we demonstrate that MPSs with short-range correlations can be prepared with shallow circuits by leveraging heuristics from approximate quantum compiling (AQC). We achieve this with ADAPT-AQC, an adaptive-ansatz preparation algorithm, and introduce a generalised initialisation procedure for the existing AQC-Tensor algorithm. We first compare these methods for the task of preparing a molecular electronic structure ground state. We then use them to prepare an antiferromagnetic (AFM) ground state of the 50-site Heisenberg XXZ spin chain near the AFM-XY phase boundary. Through the execution of circuits with up to 59 CZ depth and 1251 CZ gates, we perform a global quench and observe the relaxation of magnetic ordering in a parameter regime previously inaccessible due to deep ground state preparation circuits. Our results demonstrate how the integration of quantum and classical resources can push the boundary of what can be studied on quantum computers.

Long-range bipartite entanglement in XXZ spin chains with the exponential and power-law long-range interactions

Authors: Na Li, Yang Zhao, Wen-Long Ma, Z. D. Wang, Yan-Kui Bai

arXiv ID: 2503.09169 | Date: 2025-03-12

Abstract: Long-range bipartite entanglement (LBE) and its distribution properties are studied in XXZ spin chains with the exponential and power-law long-range interactions (ELRIs and PLRIs). LBE quantified by two-qubit concurrence decays exponentially along with two-site distance in the infinite chain with ELRIs in the thermodynamic limit, and the long-range behavior of two-spin entanglement can detect the quantum phase transition and identify different quantum phases away from the critical point. Moreover, a fine-grained LBE distribution relation is obtained for the infinite XXZ spin chain. On the other hand, in the finite XXZ spin chain with the conventional PLRIs, the long-range concurrence decays algebraically and the total one is no longer monotonic along with the chain length. The total LBE distribution property can exhibit a piecewise function, which has a close relationship with the decaying mode and strength of PLRIs. These LBE relations can be regarded as the generalization of Koashi-Bužek-Imoto bound for the prototypical long-range XXZ model, having potential applications in quantum information processing.

Towards Excitations and Dynamical Quantities in Correlated Lattices with Density Matrix Embedding Theory

Authors: Shuoxue Li, Chenghan Li, Huanchen Zhai, Garnet Kin-Lic Chan

arXiv ID: 2503.08880 | Date: 2025-03-11

Abstract: Density matrix embedding theory (DMET) provides a framework to describe ground-state expectation values in strongly correlated systems, but its extension to dynamical quantities is still an open problem. We show one route to obtaining excitations and dynamical spectral functions by using the techniques of DMET to approximate the matrix elements that arise in a single-mode inspired excitation ansatz. We demonstrate this approach in the 1D Hubbard model, comparing the neutral excitations, single-particle density of states, charge, and spin dynamical structure factors to benchmarks from the Bethe ansatz and density matrix renormalization group. Our work highlights the potential of these ideas in building computationally efficient approaches for dynamical quantities.

A Tutorial on Knots and Quantum Mechanics

Authors: Dmitry Melnikov

arXiv ID: 2503.08846 | Date: 2025-03-11

Abstract: These notes review a description of quantum mechanics in terms of the topology of spaces, basing on the axioms of Topological Quantum Field Theory and path integral formalism. In this description quantum states and operators are encoded by the topology of spaces that are used as modules to build the quantum mechanical model, while expectation values and probabilities are given by topological invariants of spaces, knots and links. The notes focus on the specific way the topology encodes quantum mechanical features, or, equivalently, on how these features can be controlled through the topology. A topological classification of entanglement is discussed, as well as properties of entanglement entropy and basic quantum protocols. The primary aim is to build a less conventional diagrammatic intuition about quantum mechanics, expanding the paradigm of ``Quantum Picturalism".

Circuits as a simple platform for the emergence of hydrodynamics in deterministic chaotic many-body systems

Authors: Sun Woo P. Kim, Friedrich Hübner, Juan P. Garrahan, Benjamin Doyon

arXiv ID: 2503.08788 | Date: 2025-03-11

Abstract: The emergence of hydrodynamics is one of the deepest phenomena in many-body systems. Arguably, the hydrodynamic equations are also the most important tools for predicting large-scale behaviour. Understanding how such equations emerge from microscopic deterministic dynamics is a century-old problem, despite recent progress in fine-tuned integrable systems. Due to the universality of hydrodynamics, the specific microscopic implementation should not matter. Here, we show that classical deterministic circuits provide a minimal, exact, and efficient platform that admits non-trivial hydrodynamic behaviour for deterministic but chaotic systems. By developing new techniques and focusing on 1D circuits as a proof of concept, we obtain the characteristic dynamics, including relaxation to Gibbs states, exact Euler equations, shocks, diffusion, and exact KPZ super-diffusion. Our methods can be easily generalised to higher dimensions or quantum circuits.

Combining Local Symmetry Exploitation and Reinforcement Learning for Optimised Probabilistic Inference -- A Work In Progress

Authors: Sagad Hamid, Tanya Braun

arXiv ID: 2503.08786 | Date: 2025-03-11

Abstract: Efficient probabilistic inference by variable elimination in graphical models requires an optimal elimination order. However, finding an optimal order is a challenging combinatorial optimisation problem for models with a large number of random variables. Most recently, a reinforcement learning approach has been proposed to find efficient contraction orders in tensor networks. Due to the duality between graphical models and tensor networks, we adapt this approach to probabilistic inference in graphical models. Furthermore, we incorporate structure exploitation into the process of finding an optimal order. Currently, the agent's cost function is formulated in terms of intermediate result sizes which are exponential in the number of indices (i.e., random variables). We show that leveraging specific structures during inference allows for introducing compact encodings of intermediate results which can be significantly smaller. By considering the compact encoding sizes for the cost function instead, we enable the agent to explore more efficient contraction orders. The structure we consider in this work is the presence of local symmetries (i.e., symmetries within a model's factors).

Robust Simulations of Many-Body Symmetry-Protected Topological Phase Transitions on a Quantum Processor

Authors: Ruizhe Shen, Tianqi Chen, Bo Yang, Yin Zhong, Ching Hua Lee

arXiv ID: 2503.08776 | Date: 2025-03-11

Abstract: Topology and symmetry play critical roles in characterizing quantum phases of matter. Recent advancements have unveiled symmetry-protected topological (SPT) phases in many-body systems as a unique class of short-range entangled states, notable for their nontrivial edge modes and characteristic ground-state entanglement gap. In this study, we demonstrate the robust simulation of many-body ground states of an Ising-cluster model on a quantum computer. By employing the method of quantum imaginary-time evolution (QITE) combined with enhanced zero-noise extrapolation techniques, we achieve accurate measurements of the transition between trivial and cluster SPT phases. Furthermore, we measured the characteristic edge modes and their associated topological entanglement properties, such as the second Rényi entropy, reduced density matrix, and entanglement spectral gap. Our work demonstrates the potential of using QITE in investigating sophisticated quantum phase transitions and critical phenomena on quantum computers.

Tensor networks for quantum computing

Authors: Aleksandr Berezutskii, Minzhao Liu, Atithi Acharya, Roman Ellerbrock, Johnnie Gray, Reza Haghshenas, Zichang He, Abid Khan, Viacheslav Kuzmin, Dmitry Lyakh, Danylo Lykov, Salvatore Mandrà, Christopher Mansell, Alexey Melnikov, Artem Melnikov, Vladimir Mironov, Dmitry Morozov, Florian Neukart, Alberto Nocera, Michael A. Perlin, Michael Perelshtein, Matthew Steinberg, Ruslan Shaydulin, Benjamin Villalonga, Markus Pflitsch, Marco Pistoia, Valerii Vinokur, Yuri Alexeev

arXiv ID: 2503.08626 | Date: 2025-03-11

Abstract: In the rapidly evolving field of quantum computing, tensor networks serve as an important tool due to their multifaceted utility. In this paper, we review the diverse applications of tensor networks and show that they are an important instrument for quantum computing. Specifically, we summarize the application of tensor networks in various domains of quantum computing, including simulation of quantum computation, quantum circuit synthesis, quantum error correction and mitigation, and quantum machine learning. Finally, we provide an outlook on the opportunities and the challenges of the tensor-network techniques.

A hybrid method integrating Green's function Monte Carlo and projected entangled pair states

Authors: He-Yu Lin, Rong-Qiang He, Yibin Guo, Zhong-Yi Lu

arXiv ID: 2503.08450 | Date: 2025-03-11

Abstract: This paper introduces a hybrid approach combining Green's function Monte Carlo (GFMC) method with projected entangled pair state (PEPS) ansatz. This hybrid method regards PEPS as a trial state and a guiding wave function in GFMC. By leveraging PEPS's proficiency in capturing quantum state entanglement and GFMC's efficient parallel architecture, the hybrid method is well-suited for the accurate and efficient treatment of frustrated quantum spin systems. As a benchmark, we applied this approach to study the frustrated J1J_1-J2J_2 Heisenberg model on a square lattice with periodic boundary conditions (PBC). Compared with other numerical methods, our approach integrating PEPS and GFMC shows competitive accuracy in the performance of ground-state energy. This paper provides systematic and comprehensive discussion of the approach of our previous work.

Fully numerical Hartree-Fock calculations for atoms and small molecules with quantics tensor trains

Authors: Paul Haubenwallner, Matthias Heller

arXiv ID: 2503.08430 | Date: 2025-03-11

Abstract: We present a fully numerical framework for the optimization of molecule-specific quantum chemical basis functions within the quantics tensor train format using a finite-difference scheme. The optimization is driven by solving the Hartree-Fock equations (HF) with the density-matrix renormalization group (DMRG) algorithm on Cartesian grids that are iteratively refined. In contrast to the standard way of tackling the mean-field problem by expressing the molecular orbitals as linear combinations of atomic orbitals (LCAO) our method only requires as much basis functions as there are electrons within the system. Benchmark calculations for atoms and molecules with up to ten electrons show excellent agreement with LCAO calculations with large basis sets supporting the validity of the tensor network approach. Our work therefore offers a promising alternative to well-established HF-solvers and could pave the way to define highly accurate, fully numerical, molecule-adaptive basis sets, which, in the future, could lead to benefits for post-HF calculations.

Altermagnetism and beyond in the tt-tt^\prime-δδ Fermi-Hubbard model

Authors: Saisai He, Jize Zhao, Hong-Gang Luo, Shijie Hu

arXiv ID: 2503.08362 | Date: 2025-03-11

Abstract: In this work, we revisit the phase diagram of the tt-tt^\prime-δδ Fermi-Hubbard model on the square lattice to gain a more comprehensive understanding of this correlated model at half filling. This model has recently become a prominent topic of research because it hosts altermagnetic phases. Using mean-field analysis, we identify four metallic phases and two insulating phases with nontrivial magnetic orders at an intermediate value of δ=0.5δ= 0.5, presenting a rich ground-state phase diagram in the UU-tt^\prime plane. We also highlight the distinct features of the Fermi surface topology for each metallic phase. To go beyond the mean-field theory, we employ the density-matrix renormalization group method to simulate the ground state numerically. The phase boundaries are determined from the discontinuities and peaks in the entanglement entropy and magnetizations. In addition to the phases identified in the mean-field theory, we find a valence-bond solid state in a narrow intermediate-tt' region. Our work offers a firm step forward in understanding the complex behaviors of correlated electrons in the tt-tt^\prime-δδ Hubbard model over a large parameter space.

Challenging the Quantum Advantage Frontier with Large-Scale Classical Simulations of Annealing Dynamics

Authors: Linda Mauron, Giuseppe Carleo

arXiv ID: 2503.08247 | Date: 2025-03-11

Abstract: Recent demonstrations of D-Wave's annealing-based quantum simulators have established new benchmarks for quantum computational advantage [arXiv:2403.00910]. However, the precise location of the classical-quantum computational frontier remains an open question, as classical simulation strategies continue to evolve. Here, we demonstrate that time-dependent variational Monte Carlo (t-VMC) with a physically motivated Jastrow-Feenberg wave function can efficiently simulate the quantum annealing of spin glasses up to system sizes previously thought to be intractable. Our approach achieves accuracy comparable to that of quantum processing units while requiring only polynomially scaling computational resources, in stark contrast to entangled-limited tensor network methods that scale exponentially. For systems up to 128 spins on a three-dimensional diamond lattice, we maintain correlation errors below 7%, which match or exceed the precision of existing quantum hardware. Rigorous assessments of residual energies and time-dependent variational principle errors establish clear performance benchmarks for classical simulations. These findings substantially shift the quantum advantage frontier and underscore that classical variational techniques, which are not fundamentally constrained by entanglement growth, remain competitive at larger system sizes than previously anticipated.

Counting with the quantum alternating operator ansatz

Authors: Julien Drapeau, Shreya Banerjee, Stefanos Kourtis

arXiv ID: 2503.07720 | Date: 2025-03-10

Abstract: We introduce a variational algorithm based on the quantum alternating operator ansatz (QAOA) for the approximate solution of computationally hard counting problems. Our algorithm, dubbed VQCount, is based on the equivalence between random sampling and approximate counting and employs QAOA as a solution sampler. We first prove that VQCount improves upon previous work by reducing exponentially the number of samples needed to obtain an approximation within a multiplicative factor of the exact count. Using tensor network simulations, we then study the typical performance of VQCount with shallow circuits on synthetic instances of two #P-hard problems, positive #NAE3SAT and positive #1-in-3SAT. We employ the original quantum approximate optimization algorithm version of QAOA, as well as the Grover-mixer variant which guarantees a uniform solution probability distribution. We observe a tradeoff between QAOA success probability and sampling uniformity, which we exploit to achieve an exponential gain in efficiency over naive rejection sampling. Our results highlight the potential and limitations of variational algorithms for approximate counting.

Robustness of Vacancy-Bound Non-Abelian Anyons in the Kitaev Model in a Magnetic Field

Authors: Bo Xiao, Gonzalo Alvarez, Gábor B. Halász

arXiv ID: 2503.07716 | Date: 2025-03-10

Abstract: Non-Abelian anyons in quantum spin liquids (QSLs) provide a promising route to fault-tolerant topological quantum computation. In the exactly solvable Kitaev honeycomb model, such anyons of the QSL state can be bound to nonmagnetic spin vacancies and endowed with non-Abelian statistics by an infinitesimal magnetic field. Here, we investigate how this approach for stabilizing non-Abelian anyons extends to a finite magnetic field represented by a proper Zeeman term. Through large-scale density-matrix renormalization group (DMRG) simulations, we compute the vacancy-anyon binding energy as a function of magnetic field for both the ferromagnetic (FM) and antiferromagnetic (AFM) Kitaev models. We find that anyon binding remains robust within the entire QSL phase for the FM Kitaev model but breaks down already inside this phase for the AFM Kitaev model. To compute a binding energy several orders of magnitude below the magnetic energy scale, we introduce both a refined definition and an extrapolation scheme based on carefully tailored perturbations.

Quantum phase diagram of the spin-12\frac{1}{2} Heisenberg antiferromagnet on the square-kagome lattice: a tensor network study

Authors: Saeed S. Jahromi, Yasir Iqbal

arXiv ID: 2503.07689 | Date: 2025-03-10

Abstract: We assess the quantum phase diagram of the spin-1/21/2 Heisenberg antiferromagnetic model on the square-kagome lattice upon varying the two symmetry inequivalent nearest-neighbor couplings, J1J_{1} on squares and JJ on triangles. Employing large-scale tensor network simulations based on infinite projected entangled pair states, we find four distinct valence bond crystal (VBC) states and a ferrimagnetically ordered region. Starting from the limit of weakly interacting squares for small J/J1J/J_{1} where a plaquette cross-dimer VBC with long-range singlets is stabilized, we show that with increasing J/J1J/J_{1} it transitions to a VBC with resonances over hexagons, the so-called loop-six VBC, which persists across the isotropic point. Interestingly, a generalized version of the pinwheel VBC, earlier reported to be a closely competing state for the isotropic model is energetically stabilized in a sliver of parameter space right beyond the isotropic point. For further increases in J/J1J/J_{1}, a decorated loop-six VBC occupies an appreciable region of parameter space before transitioning into an imperfect ferrimagnet which finally evolves into a Lieb ferrimagnet. Our characterization of the underlying phases and phase transitions is based on a careful analysis of the energy, magnetization, spin-spin correlations, and bond entanglement entropy.

Dynamics of Matrix Product States in the Heisenberg Picture: Projectivity, Ergodicity, and Mixing

Authors: Abdessatar Souissi, Amenallah Andolsi

arXiv ID: 2503.06546 | Date: 2025-03-09

Abstract: This paper introduces a Heisenberg picture approach to Matrix Product States (MPS), offering a rigorous yet intuitive framework to explore their structure and classification. MPS efficiently represent ground states of quantum many-body systems, with infinite MPS (iMPS) capturing long-range correlations and thermodynamic behavior. We classify MPS into projective and non-projective types, distinguishing those with finite correlation structures from those requiring ergodic quantum channels to define a meaningful limit. Using the Markov-Dobrushin inequality, we establish conditions for infinite-volume states and introduce ergodic and mixing MPS. As an application, we analyze the depolarizing MPS, highlighting its lack of finite correlations and the need for an alternative ergodic description. This work deepens the mathematical foundations of MPS and iMPS, providing new insights into entanglement, phase transitions, and quantum dynamics.

Tensor Learning and Compression of N-phonon Interactions

Authors: Yao Luo, Dhruv Mangtani, Shiyu Peng, Jia Yao, Sergei Kliavinek, Marco Bernardi

arXiv ID: 2503.05913 | Date: 2025-03-07

Abstract: Phonon interactions from lattice anharmonicity govern thermal properties and heat transport in materials. These interactions are described by n-th order interatomic force constants (n-IFCs), which can be viewed as high-dimensional tensors correlating the motion of n atoms, or equivalently encoding n-phonon scattering processes in momentum space. Here, we introduce a tensor decomposition to efficiently compress n-IFCs for arbitrary order n. Using tensor learning, we find optimal low-rank approximations of n-IFCs by solving the resulting optimization problem. Our approach reveals the inherent low dimensionality of phonon-phonon interactions and allows compression of the 3 and 4-IFC tensors by factors of up to 10310410^3-10^4 while retaining high accuracy in calculations of phonon scattering rates and thermal conductivity. Calculations of thermal conductivity using the compressed n-IFCs achieve a speed-up by nearly three orders of magnitude with >98% accuracy relative to the reference uncompressed solution. These calculations include both 3- and 4-phonon scattering and are shown for a diverse range of materials (Si, HgTe, MgO, TiNiSn and monoclinic ZrO2_2). In addition to accelerating state-of-the-art thermal transport calculations, the method shown here paves the way for modeling strongly anharmonic materials and higher-order phonon interactions.

Quantum State Designs from Minimally Random Quantum Circuits

Authors: Jonathon Riddell, Katja Klobas, Bruno Bertini

arXiv ID: 2503.05698 | Date: 2025-03-07

Abstract: Random many-body states are both a useful tool to model certain physical systems and an important asset for quantum computation. Realising them, however, generally requires an exponential (in system size) amount of resources. Recent research has presented a way out by showing that one can generate random states, or more precisely a controlled approximation of them, by applying a quantum circuit built in terms of few-body unitary gates. Most of this research, however, has been focussed on the case of quantum circuits composed by completely random unitary gates. Here we consider what happens for circuits that, instead, involve a minimal degree of randomness. Specifically, we concentrate on two different settings: (a) brickwork quantum circuits with a single one-qudit random matrix at a boundary; (b) brickwork quantum circuits with fixed interactions but random one-qudit gates everywhere. We show that, for any given initial state, (a) and (b) produce a distribution of states approaching the Haar distribution in the limit of large circuit depth. More precisely, we show that the moments of the distribution produced by our circuits can approximate the ones of the Haar distribution in a depth proportional to the system size. Interestingly we find that in both Cases (a) and (b) the relaxation to the Haar distribution occurs in two steps - this is in contrast with what happens in fully random circuits. Moreover, we show that choosing appropriately the fixed interactions, for example taking the local gate to be a dual-unitary gate with high enough entangling power, minimally random circuits produce a Haar random distribution more rapidly than fully random circuits. In particular, dual-unitary circuits with maximal entangling power - i.e. perfect tensors - appear to provide the optimal quantum state design preparation for any design number.

Dynamics of disordered quantum systems with two- and three-dimensional tensor networks

Authors: Joseph Tindall, Antonio Mello, Matt Fishman, Miles Stoudenmire, Dries Sels

arXiv ID: 2503.05693 | Date: 2025-03-07

Abstract: Quantum spin glasses form a good testbed for studying the performance of various quantum annealing and optimization algorithms. In this work we show how two- and three-dimensional tensor networks can accurately and efficiently simulate the quantum annealing dynamics of Ising spin glasses on a range of lattices. Such dynamics were recently simulated using D-Wave's Advantage22 system [A. D. King et al, Science, 10.1126/science.ado6285 (2025)] and, following extensive comparisons to existing numerical methods, claimed to be beyond the reach of classical computation. Here we show that by evolving lattice-specific tensor networks with simple belief propagation to keep up with the entanglement generated during the time evolution and then extracting expectation values with more sophisticated variants of belief propagation, state-of-the-art accuracies can be reached with modest computational resources. We exploit the scalability of our simulations and simulate a system of over 300300 qubits, allowing us to verify the universal physics present and extract a value for the associated Kibble-Zurek exponent which agrees with recent values obtained in literature. Our results demonstrate that tensor networks are a viable approach for simulating large scale quantum dynamics in two and three dimensions on classical computers, and algorithmic advancements are expected to expand their applicability going forward.

Less Quantum, More Advantage: An End-to-End Quantum Algorithm for the Jones Polynomial

Authors: Tuomas Laakkonen, Enrico Rinaldi, Chris N. Self, Eli Chertkov, Matthew DeCross, David Hayes, Brian Neyenhuis, Marcello Benedetti, Konstantinos Meichanetzidis

arXiv ID: 2503.05625 | Date: 2025-03-07

Abstract: We present an end-to-end reconfigurable algorithmic pipeline for solving a famous problem in knot theory using a noisy digital quantum computer, namely computing the value of the Jones polynomial at the fifth root of unity within additive error for any input link, i.e. a closed braid. This problem is DQC1-complete for Markov-closed braids and BQP-complete for Plat-closed braids, and we accommodate both versions of the problem. Even though it is widely believed that DQC1 is strictly contained in BQP, and so is 'less quantum', the resource requirements of classical algorithms for the DQC1 version are at least as high as for the BQP version, and so we potentially gain 'more advantage' by focusing on Markov-closed braids in our exposition. We demonstrate our quantum algorithm on Quantinuum's H2-2 quantum computer and show the effect of problem-tailored error-mitigation techniques. Further, leveraging that the Jones polynomial is a link invariant, we construct an efficiently verifiable benchmark to characterise the effect of noise present in a given quantum processor. In parallel, we implement and benchmark the state-of-the-art tensor-network-based classical algorithms for computing the Jones polynomial. The practical tools provided in this work allow for precise resource estimation to identify near-term quantum advantage for a meaningful quantum-native problem in knot theory.

Harnessing Quantum Dynamics for Robust and Scalable Quantum Extreme Learning Machines

Authors: Payal D. Solanki, Anh Pham

arXiv ID: 2503.05535 | Date: 2025-03-07

Abstract: Quantum Extreme Learning Machine (QELM) is an emerging hybrid quantum machine learning framework that leverages quantum system dynamics to enhance classical models. However, QELM can suffer from the exponential concentration problem, where excessive entanglement reduces model expressivity. In this work, we gain insight into this challenge and demonstrate how tensor network methods specifically, the Time Dependent Variational Principle (TDVP) with Matrix Product States (MPS) can efficiently simulate quantum systems while controlling entanglement and mitigating exponential concentration. Using numerical experiments on the Modified National Institute of Standards and Technology (MNIST) dataset, we show that time-evolving an MPS system modeled as a chain of Rydberg atoms produces high-quality data embeddings with low classical computational overhead. Our findings indicate that exact simulation of quantum dynamics is not necessary for strong machine learning performance; even approximate quantum embeddings can yield competitive results. Furthermore, we observe that both increased disorder in the quantum state achieved by tuning Hamiltonian parameters and careful control of entanglement directly correlate with improved model accuracy, highlighting the importance of these factors in optimizing QELM performance.

Preparing Code States via Seed-Entangler-Enriched Sequential Quantum Circuits: Application to Tetra-Digit Topological Error-Correcting Codes

Authors: Yu-Tao Hu, Meng-Yuan Li, Peng Ye

arXiv ID: 2503.05374 | Date: 2025-03-07

Abstract: Demonstrating how long-range entangled states are born from product states has gained much attention, which is not only important for quantum technology but also provides an unconventional tool in characterizing and classifying exotic phases of matter. In this paper, we introduce a unified and efficient framework of quantum circuits (i.e., a series of local unitary transformations), termed the \emph{Seed-Entangler-Enriched Sequential Quantum Circuit} (SEESQC) to construct long-range entangled states (i.e., code states) in code space of topological error-correcting codes. Specifically, we apply SEESQC to construct code states of Tetra-Digit models -- a broad class of long-range entangled stabilizer codes indexed by a four-digit parameter. These models are not rare but encompass Toric Codes across arbitrary dimensions and subsume the X-cube fracton code as special cases. Featuring a hierarchical structure of generalized entanglement renormalization group, many Tetra-Digit models host spatially extended excitations (e.g., loops, membranes, and exotic non-manifold objects) with constrained mobility and deformability, and exhibit system-size-dependent ground state degeneracies that scale exponentially with a polynomial in linear sizes. In this work, we begin with graphical and algebraic demonstration of quantum circuits for computational basis states, before generalizing to broader cases. Central to this framework is a key ingredient termed the \emph{seed-entangler} acting on a small number of qubits termed \textit{seeds}, enabling a systematic scheme to achieve arbitrary code states. Remarkably, the number of available seeds equals the number of logical qubits for the constructed examples, which leaves plenty of room for future investigation in theoretical physics, mathematics and quantum information science. Beyond the critical limitation of prior state-engineering methodologies, ...

Critical endpoints of three-dimensional finite density SU(3) spin model with tensor renormalization group

Authors: Xiao Luo, Yoshinobu Kuramashi

arXiv ID: 2503.05144 | Date: 2025-03-07

Abstract: We investigate the phase diagram of the three-dimensional SU(3) spin model with finite chemical potential, which is an effective Polyakov loop model for finite density QCD, using the tensor renormalization group method. We successfully determine the location of the critical endpoints being free from the complex action problem in the standard Monte Carlo approach. The critical values of the parameters show the consistency with previous ones obtained by other analytic and numerical methods.

Entanglement Transitions in Noisy Quantum Circuits on Trees

Authors: Vikram Ravindranath, Yiqiu Han, Xiao Chen

arXiv ID: 2503.05027 | Date: 2025-03-06

Abstract: Decoherence is ubiquitous, and poses a significant impediment to the observation of quantum phenomena, such as the measurement-induced entanglement phase transition (MIPT). In this work, we study entanglement transitions in quantum circuits on trees, subject to both noise and measurements. We uncover a rich phase diagram that describes the ability of a tree quantum circuit to retain quantum or classical information in the presence of decoherence. By developing a mapping between the dynamics of information on the tree to a classical Markov process -- also defined on the tree -- we obtain exact solutions to the entanglement transitions displayed by the circuit under various noise and measurement strengths. Moreover, we find a host of phenomena, including the MIPT, which are \textit{robust} to decoherence. The analytical tractability facilitated by the method developed in this paper showcases the first example of an exactly solvable noise-robust MIPT, and holds promise for studies on broader, tree-like circuits.

Detection of 2D SPT Order with Partial Symmetries

Authors: Alex Turzillo, Naren Manjunath, Jose Garre-Rubio

arXiv ID: 2503.04510 | Date: 2025-03-06

Abstract: A method of using partial symmetries to distinguish two dimensional symmetry protected topological (SPT) phases of on-site, unitary symmetries is proposed. This novel order parameter takes a wavefunction, such as a ground state of a lattice model, and detects its SPT invariants as expectation values of finitely supported operators, without the need for flux insertion. The construction exploits the rotational symmetry of the lattice to extract on-site SPT invariants, building upon prior work on probing crystalline SPT phases with partial rotations. The method is demonstrated by computing the order parameter analytically on group cohomology models and numerically on a family of states interpolating between the CZX state and a trivial state. Its robustness is suggested by interpreting partial symmetries as generating the topological partition functions of lens spaces.

Tensor Network Techniques for Quantum Computation

Authors: Mario Collura, Guglielmo Lami, Nishan Ranabhat, Alessandro Santini

arXiv ID: 2503.04423 | Date: 2025-03-06

Abstract: This book serves as an introductory yet thorough guide to tensor networks and their applications in quantum computation and quantum information, designed for advanced undergraduate and graduate-level readers. In Part I, foundational topics are covered, including tensor structures and network representations like Matrix Product States (MPS) and Tree Tensor Networks (TTN). These preliminaries provide readers with the core mathematical tools and concepts necessary for quantum physics and quantum computing applications, bridging the gap between multi-linear algebra and complex quantum systems. Part II explores practical applications of tensor networks in simulating quantum dynamics, with a particular focus on the efficiency they offer for systems of high computational complexity. Key topics include Hamiltonian dynamics, quantum annealing, open system dynamics, and optimization strategies using TN frameworks. A final chapter addresses the emerging role of "quantum magic" in tensor networks. It delves into non-stabilizer states and their contribution to quantum computational power beyond classical simulability, featuring methods such as stabilizer-enhanced MPS and the Clifford-dressed TDVP.

Self-consistent tensor network method for correlated super-moiré matter beyond one billion sites

Authors: Yitao Sun, Marcel Niedermeier, Tiago V. C. Antão, Adolfo O. Fumega, Jose L. Lado

arXiv ID: 2503.04373 | Date: 2025-03-06

Abstract: Moiré and super-moiré materials provide exceptional platforms to engineer exotic correlated quantum matter. The vast number of sites required to model moiré systems in real space remains a formidable challenge due to the immense computational resources required. Super-moiré materials push this requirement to the limit, where millions or even billions of sites need to be considered, a requirement beyond the capabilities of conventional methods for interacting systems. Here, we establish a methodology that allows solving correlated states in systems reaching a billion sites, that exploits tensor-network representations of real-space Hamiltonians and self-consistent real-space mean-field equations. Our method combines a tensor-network kernel polynomial method with quantics tensor cross interpolation algorithm, enabling us to solve exponentially large models, including those whose single particle Hamiltonian is too large to be stored explicitly. We demonstrate our methodology with super-moiré systems featuring spatially modulated hoppings, many-body interactions and domain walls, showing that it allows access to self-consistent symmetry broken states and spectral functions of real-space models reaching a billion sites. Our methodology provides a strategy to solve exceptionally large interacting problems, providing a widely applicable strategy to compute correlated super-moiré quantum matter.

Image Computation for Quantum Transition Systems

Authors: Xin Hong, Dingchao Gao, Sanjiang Li, Shenggang Ying, Mingsheng Ying

arXiv ID: 2503.04146 | Date: 2025-03-06

Abstract: With the rapid progress in quantum hardware and software, the need for verification of quantum systems becomes increasingly crucial. While model checking is a dominant and very successful technique for verifying classical systems, its application to quantum systems is still an underdeveloped research area. This paper advances the development of model checking quantum systems by providing efficient image computation algorithms for quantum transition systems, which play a fundamental role in model checking. In our approach, we represent quantum circuits as tensor networks and design algorithms by leveraging the properties of tensor networks and tensor decision diagrams. Our experiments demonstrate that our contraction partition-based algorithm can greatly improve the efficiency of image computation for quantum transition systems.

Tight and self-testing multipartite quantum Bell inequalities from the renormalization group

Authors: Paolo Abiuso, Julian Fischer, Miguel Navascués

arXiv ID: 2503.03878 | Date: 2025-03-05

Abstract: In past work, the concept of connectors was introduced: directed tensors with the property that any contraction thereof defines a multipartite quantum Bell inequality, i.e., a linear restriction on measurement probabilities that holds in any multipartite quantum experiment. In this paper we propose the notion of ''tight connectors'', which, if contracted according to some simple rules, result in tight quantum Bell inequalities. By construction, the new inequalities are saturated by tensor network states, whose structure mimics the corresponding network of connectors. Some tight connectors are furthermore ''fully self-testing'', which implies that the quantum Bell inequalities they generate can only be maximized with such a tensor network state and specific measurement operators (modulo local isometries). We provide large analytic families of tight, fully self-testing connectors that generate NN-partite quantum Bell inequalities of correlator form for which the ratio between the maximum quantum and classical values increases exponentially with NN.

Constrained many-body phases in a Z2\mathbb{Z}_2-Higgs lattice gauge theory

Authors: Alexander Schuckert, Stefan Kühn, Kevin C. Smith, Eleanor Crane, Steven M. Girvin

arXiv ID: 2503.03828 | Date: 2025-03-05

Abstract: We study the ground-state phase diagram of a one-dimensional Z2\mathbb{Z}_2 lattice gauge theory coupled to soft-core bosonic matter at unit filling, inspired by the Higgs sector of the standard model. Through a combination of analytical perturbative approaches, exact diagonalization, and density-matrix-renormalization-group simulations, we uncover a rich phase diagram driven by gauge-field-mediated resonant pair hopping and the confinement of single particles. The pair hopping results in a bunching state with superextensive energy and macroscopic particle number fluctuations at strong electric field strengths and weak on-site interactions. The bunching state crosses over into a pair superfluid phase as the on-site interaction increases, characterized by a finite superfluid density and powerlaw-decaying pair correlations. At large on-site interaction strengths and driven by effective interactions induced by the gauge constraint, the superfluid transitions into an incompressible pair Mott insulator phase. At weak field strengths and on-site interactions, we find a plasma-like region, where single bosons exhibit large short-range correlations and the ground state is composed almost equally of states with even and odd local boson occupation. The presence of a bunching state with large number fluctuations, which is difficult to study using classical numerics, motivates experimental realizations in hybrid boson-qubit quantum simulation platforms such as circuit QED, neutral atoms, and trapped ions. Our findings highlight the rich interplay between gauge fields and soft-core bosonic matter.

Beginner's Lecture Notes on Quantum Spin Chains, Exact Diagonalization and Tensor Networks

Authors: Guglielmo Lami, Mario Collura, Nishan Ranabhat

arXiv ID: 2503.03564 | Date: 2025-03-05

Abstract: Aimed at introducing readers to the physics of strongly correlated many-body systems, these notes focus on numerical methods, with detailed discussions on implementing working code for exact diagonalization. A brief introduction to tensor network methods is also included. Prepared for the Summer School Quantumandu, held at Tribhuvan University (Kathmandu, Nepal) from 25 to 31 July 2024, as part of the ICTP's Physics Without Frontiers program, these notes are primarily intended for readers encountering this field for the first time.

Steady-state dynamical mean field theory based on influence functional matrix product states

Authors: Mithilesh Nayak, Julian Thoenniss, Michael Sonner, Dmitry A. Abanin, Philipp Werner

arXiv ID: 2503.02848 | Date: 2025-03-04

Abstract: We implement the recently developed influence functional matrix product states approach as impurity solver in equilibrium and nonequilibrium dynamical mean field theory (DMFT) calculations of the single-band Hubbard model. The method yields numerically exact descriptions of metallic states without sharp spectral features, at a moderate numerical cost. Systems with narrow quasiparticle or spin-polaron peaks, as well as low-temperature Mott insulators provide more challenges, since these simulations require long time contours or high bond dimensions. A promising field of application is the DMFT simulation of nonequilibrium steady states, which we demonstrate with results for photo-doped Mott systems with long-lived doublon and holon populations.

Ground State of SU(3)\mathrm{SU}\left(3\right) spin model on the checkerboard lattice

Authors: Junhao Zhang, Jie Hou, Jie Lou, Yan Chen

arXiv ID: 2503.02805 | Date: 2025-03-04

Abstract: Geometric frustration in quantum spin systems can lead to exotic ground states. In this study, we investigate the SU(3)\mathrm{SU}(3) spin model on the checkerboard lattice to explore the effects of frustration arising from its point-connected (N+1)(N+1)-site local structure. We employ density matrix renormalization group (DMRG) and exact diagonalization (ED) techniques to determine the ground state properties. Our results reveal the absence of both 3-sublattice antiferromagnetic order and valence cluster solid order. Instead, we identify ground states with bond stripe patterns sensitive to boundary conditions and system size, comprising staggered singlet arrays and uniform flat stripes. Notably, these stripes are relatively decoupled, and similar patterns can be reconstructed in quasi-one-dimensional ladders. These findings suggest that geometric frustration drives the system toward a mixed phase, combining characteristics of spin-liquid and valence cluster solid states, providing new insights into the behavior of frustrated quantum spin systems.

Meson dynamics from locally exciting a particle-conserving Z2Z_2 lattice gauge theory

Authors: Vaibhav Sharma, Kaden R. A. Hazzard

arXiv ID: 2503.02791 | Date: 2025-03-04

Abstract: Quantum simulation of lattice gauge theories is an important avenue to gain insights into both particle physics phenomena and constrained quantum many-body dynamics. There is a growing interest in probing analogs of high energy collision phenomena in lattice gauge theories that can be implemented on current quantum simulators. Motivated by this, we characterize the confined mesons that originate from a local high energy excitation in a particle-conserving 1D Z2Z_2 lattice gauge theory. We focus on a simple, experimentally accessible setting that does not require preparation of colliding wavepackets and isolates the effects of gauge field confinement strength and initial state energy on the nature of propagating excitations. We find that the dynamics is characterized by the propagation of a superposition of differently sized mesons. The linear confinement leads to meson size oscillations in time. The average meson size and oscillation frequency are controlled by the strength of the gauge field confinement. At a constant confinement field, the average meson length is controlled by the initial excitation's energy. Higher energies produce longer mesons and their effective mass depends strongly on their size: longer mesons propagate more slowly out of the central excitation. Mesons of different sizes get spatially filtered with time due to different speeds. We show that this phenomenology is a consequence of linear confinement and remains valid in both the strong and weak confinement limit. We present simple explanations of these phenomena supported by exact numerics.

Phase diagram of a coupled trimer system at half filling using the Hubbard model

Authors: Sourabh Saha, Hosho Katsura, Manoranjan Kumar

arXiv ID: 2503.02278 | Date: 2025-03-04

Abstract: Flat band systems have recently attracted significant attention due to their instability under small perturbations, which can lead to the stabilization of many exotic quantum phases. We study a trimer ladder which shows a middle flat band in the absence of onsite Coulomb interaction. We investigate the quantum phases of the Hubbard model on this geometry using exact diagonalization (ED), density matrix renormalization group (DMRG), and perturbation theory. We construct a quantum phase diagram in the plane of the next-nearest-neighbor hopping parameter t2t_2 and onsite Coulomb interaction UU, revealing five distinct quantum phases. At low UU and moderate to high magnitude of t2t_2, the system exhibits metallic behavior, while at large UU and small magnitude of t2t_2, it transitions to a ferrimagnetic insulator phase, similar to those observed in certain trimer materials. In the small t2t_2 limit, the Fermi energy is in the flat band, leading to localization of the electrons within the trimer. At low UU and small magnitude of t2t_2, the flat band mechanism favors insulating ferrimagnetism, whereas at large UU, ferrimagnetic states emerge from singlet dimer formation between neighboring sites of a trimer and an isolated corner spin, which connect ferromagnetically. The insulating cell spin density wave phase displays an up-up-down-down spin configuration due to competing nearest neighbor hopping, t1t_1. Interestingly, in moderate UU and t2>0.3|t_2|>0.3, the ground state behaves like metallic Tomonaga-Luttinger liquid.

Self-interacting processes via Doob conditioning

Authors: Francesco Coghi, Juan P. Garrahan

arXiv ID: 2503.01574 | Date: 2025-03-03

Abstract: We connect self-interacting processes, that is, stochastic processes where transitions depend on the time spent by a trajectory in each configuration, to Doob conditioning. In this way we demonstrate that Markov processes with constrained occupation measures are realised optimally by self-interacting dynamics. We use a tensor network framework to guide our derivations. We illustrate our general results with new perspectives on well-known examples of self-interacting processes, such as random walk bridges, excursions, and forced excursions.

Compactifying Electronic Wavefunctions I: Error-Mitigated Transcorrelated DMRG

Authors: Bruna G. M. Araújo, Antonio M S Macedo

arXiv ID: 2503.00627 | Date: 2025-03-01

Abstract: Transcorrelation (TC) techniques effectively enhance convergence rates in strongly correlated fermionic systems by embedding electron-electron cusp into the Jastrow factor of similarity transformations, yielding a non-Hermitian, yet iso-spectral, Hamiltonian. This non-Hermitian nature introduces significant challenges for variational methods such as the Density Matrix Renormalization Group (DMRG). To address these, existing approaches often rely on computationally expensive methods prone to errors, such as imaginary-time evolution. We introduce an Error-Mitigated Transcorrelated DMRG (EMTC-DMRG), a classical variational algorithm that overcomes these challenges by integrating existing techniques to achieve superior accuracy and efficiency. Key features of our algorithm include: (a) an analytical formulation of the transcorrelated Fermi-Hubbard Hamiltonian; (b) a numerically exact, uncompressed Matrix Product Operator (MPO) representation developed via symbolic optimization and the Hopcroft-Karp algorithm; and (c) a time-independent DMRG with a two-site sweep algorithm; (d) we use Davidson solver even for a non-Hermitian Hamiltonian. Our method significantly enhances computational efficiency and accuracy in determining ground-state energies for the two-dimensional transcorrelated Fermi-Hubbard model with periodic boundary conditions. Additionally, it can be adapted to compute both ground and excited states in molecular systems.

Correlated hopping induced topological order in an atomic mixture

Authors: Ashirbad Padhan, Luca Barbiero, Tapan Mishra

arXiv ID: 2503.00589 | Date: 2025-03-01

Abstract: The large majority of topological phases in one dimensional many-body systems are known to inherit from the corresponding single-particle Hamiltonian. In this work, we go beyond this assumption and find a new example of topological order induced through specific interactions couplings. Specifically, we consider a fermionic mixture where one component experiences a staggered onsite potential and it is coupled through density dependent hopping interactions to the other fermionic component. Crucially, by varying the sign of the staggered potential, we show that this latter fermionic component can acquire topological properties. Thanks to matrix product state simulations, we prove this result both at the equilibrium by extracting the behavior of correlation functions and in an out-of-equilibrium scheme by employing a Thouless charge pumping. Notably, we further discuss how our results can be probed in quantum simulators made up of ultracold atoms. Our results reveal an important and alternative mechanism that can give rise to topological order.

Generating Generalised Ground-State Ansatzes from Few-Body Examples

Authors: Matt Lourens, Ilya Sinayskiy, Johannes N. Kriel, Francesco Petruccione

arXiv ID: 2503.00497 | Date: 2025-03-01

Abstract: We introduce a method that generates ground-state ansatzes for quantum many-body systems which are both analytically tractable and accurate over wide parameter regimes. Our approach leverages a custom symbolic language to construct tensor network states (TNS) via an evolutionary algorithm. This language provides operations that allow the generated TNS to automatically scale with system size. Consequently, we can evaluate ansatz fitness for small systems, which is computationally efficient, while favouring structures that continue to perform well with increasing system size. This ensures that the ansatz captures robust features of the ground state structure. Remarkably, we find analytically tractable ansatzes with a degree of universality, which encode correlations, capture finite-size effects, accurately predict ground-state energies, and offer a good description of critical phenomena. We demonstrate this method on the Lipkin-Meshkov-Glick model (LMG) and the quantum transverse-field Ising model (TFIM), where the same ansatz was independently generated for both. The simple structure of the ansatz allows us to obtain exact expressions for the expectation values of local observables as well as for correlation functions. In addition, it permits symmetries that are broken in the ansatz to be restored, which provides a systematic means of improving the accuracy of the ansatz.

Universality in the Anticoncentration of Chaotic Quantum Circuits

Authors: Arman Sauliere, Beatrice Magni, Guglielmo Lami, Xhek Turkeshi, Jacopo De Nardis

arXiv ID: 2503.00119 | Date: 2025-02-28

Abstract: We identify a \emph{universal functional form} that governs anticoncentration in random quantum circuits-one that holds across diverse circuit architectures and depths, and crucially remains valid even at finite system sizes and shallow depth. We support this claim through analytical results for ensembles of random tensor-network states and random-phase models. This compact, universal expression for the output bitstring probability distribution is fully characterized by just two fitting parameters, as validated through extensive numerical simulations. Our findings underscore the pivotal role of finite-size and finite-depth effects in shaping anticoncentration and introduce a practical framework for benchmarking quantum devices using shallow circuits, thereby enabling validation of systems significantly larger than previously accessible.

FuzzifiED : Julia Package for Numerics on the Fuzzy Sphere

Authors: Zheng Zhou

arXiv ID: 2503.00100 | Date: 2025-02-28

Abstract: The Julia package FuzzifiED aims at simplifying the numerical calculations on the fuzzy sphere. It supports exact diagonalisation (ED) and density matrix renormalisation group (DMRG) calculations. FuzzifiED can also apply to generic fermionic and bosonic models. This documentation provides a review of the fuzzy sphere regularisation and an instruction for using FuzzifiED for numerical calculations.

Quantum information elements in Quantum Gravity states and processes

Authors: Daniele Oriti

arXiv ID: 2502.21234 | Date: 2025-02-28

Abstract: We summarize basic features of quantum gravity states and processes, common to a number of related quantum gravity formalisms, and sharing a purely combinatorial and algebraic language, and a discrete geometric interpretation. We emphasize how, in this context, entanglement is a seed of topological and geometric properties, and how a pre-geometric, discrete notion of quantum causality can be implemented, as well as some recent results (based on random tensor network techniques) on the conditions for information transmission and holographic behaviour in quantum gravity states. Together, these features indicate that quantum information concepts and tools play a key role in defining the fundamental structure of quantum spacetime.

Wavelet-based density sketching with functional hierarchical tensor

Authors: Xun Tang, Lexing Ying

arXiv ID: 2502.20655 | Date: 2025-02-28

Abstract: We introduce the functional hierarchical tensor under a wavelet basis (FHT-W) ansatz for high-dimensional density estimation in lattice models. Recently, the functional tensor network has emerged as a suitable candidate for density estimation due to its ability to calculate the normalization constant exactly, a defining feature not enjoyed by neural network alternatives such as energy-based models or diffusion models. While current functional tensor network models show good performance for lattice models with weak or moderate couplings, we show that they face significant model capacity constraints when applied to lattice models with strong coupling. To address this issue, this work proposes to perform density estimation on the lattice model under a wavelet transformation. Motivated by the literature on scale separation, we perform iterative wavelet coarsening to separate the lattice model into different scales. Based on this multiscale structure, we design a new functional hierarchical tensor ansatz using a hierarchical tree topology, whereby information on the finer scale is further away from the root node of the tree. Our experiments show that the numerical rank of typical lattice models is significantly lower under appropriate wavelet transformation. Furthermore, we show that our proposed model allows one to model challenging Gaussian field models and Ginzburg-Landau models.

Anticoncentration in Clifford Circuits and Beyond: From Random Tensor Networks to Pseudo-Magic States

Authors: Beatrice Magni, Alexios Christopoulos, Andrea De Luca, Xhek Turkeshi

arXiv ID: 2502.20455 | Date: 2025-02-27

Abstract: Anticoncentration describes how an ensemble of quantum states spreads over the allowed Hilbert space, leading to statistically uniform output probability distributions. In this work, we investigate the anticoncentration of random Clifford circuits toward the overlap distribution of random stabilizer states. Using exact analytical techniques and extensive numerical simulations based on Clifford replica tensor networks, we demonstrate that random Clifford circuits fully anticoncentrate in logarithmic circuit depth, namely higher-order moments of the overlap distribution converge to those of random stabilizer states. Moreover, we investigate the effect of introducing a controlled number of non-Clifford (magic) resources into Clifford circuits. We show that inserting a polylogarithmic in qudit number of TT-states is sufficient to drive the overlap distribution toward the Porter-Thomas statistics, effectively recovering full quantum randomness. In short, this fact presents doped tensor networks and shallow Clifford circuits as pseudo-magic quantum states. Our results clarify the interplay between Clifford dynamics, magic-state injection, and quantum complexity, with implications for quantum circuit sampling, many-body quantum physics, and the benchmarking of quantum computational advantage.

Symmetry defects and gauging for quantum states with matrix product unitary symmetries

Authors: Adrián Franco-Rubio, Arkadiusz Bochniak, J. Ignacio Cirac

arXiv ID: 2502.20257 | Date: 2025-02-27

Abstract: In this work, we examine the consequences of the existence of a finite group of matrix product unitary (MPU) symmetries for matrix product states (MPS). We generalize the well-understood picture of onsite unitary symmetries, which give rise to virtual symmetry defects given by insertions of operators in the bonds of the MPS. In the MPU case, we can define analogous defect tensors, this time sitting on lattice sites, that can be created, moved, and fused by local unitary operators. We leverage this formalism to study the gauging of MPU symmetries. We introduce a condition, block independence, under which we can gauge the symmetries by promoting the symmetry defects to gauge degrees of freedom, yielding an MPS of the same bond dimension that supports a local version of the symmetry given by commuting gauge constraints. Whenever block independence does not hold (which happens, in particular, whenever the symmetry representation is anomalous), a modification of our method which we call state-level gauging still gives rise to a locally symmetric MPS by promotion of the symmetry defects, at the expense of producing gauge constraints that do not commute on different sites.

Spatio-temporal tensor-network approaches to out-of-equilibrium dynamics bridging open and closed systems

Authors: Sergio Cerezo-Roquebrún, Aleix Bou-Comas, Jan T. Schneider, Esperanza López, Luca Tagliacozzo, Stefano Carignano

arXiv ID: 2502.20214 | Date: 2025-02-27

Abstract: The study of many-body quantum systems out of equilibrium remains a significant challenge with complexity barriers arising in both state and operator-based representations. In this work, we review recent approaches based on finding better contraction strategies for the full spatio-temporal tensor networks that encode the path integral of the dynamics, as well as the conceptual integration of influence functionals, process tensors, and transfer matrices within the tensor network formalism. We discuss recent algorithmic developments, highlight the complexity of influence functionals in various dynamical regimes and present consistent results of different communities, showing how ergodic dynamics render these functionals exponentially difficult to compress. Finally, we provide an outlook on strategies to encode complementary influence functional overlaps, paving the way for accurate descriptions of open and closed quantum systems with tensor networks.

Highly Entangled 2D Ground States: Tensor Network, Order Parameter and Correlation

Authors: Olai B. Mykland, Zhao Zhang

arXiv ID: 2502.20192 | Date: 2025-02-27

Abstract: In this article we present analytical results on the exact tensor network representations and correlation functions of the first examples of 2D ground states with quantum phase transitions between area law and extensive entanglement entropy. The tensor networks constructed are one dimension higher than the lattices of the physical systems, allowing entangled physical degrees of freedoms to be paired with one another arbitrarily far away. Contraction rules of the internal legs are specified by a simple translationally invariant set of rules in terms of the tesselation of cubes or prisms in 3D space. The networks directly generalize the previous holographic tensor networks for 1D Fredkin and Motzkin chains. We also analyze the correlation in the spin and color sectors from the scaling of the height function of random surfaces, revealing additional characterizations of the exotic phase transitions.

Simulating Bulk Gap in Chiral Projected Entangled-Pair States

Authors: Ji-Yao Chen, Yi Tan, Sylvain Capponi, Didier Poilblanc, Fei Ye, Jia-Wei Mei

arXiv ID: 2502.20142 | Date: 2025-02-27

Abstract: Projected entangled-pair states (PEPS) have proven effective in capturing chiral spin liquid ground states, yet the presence of long-range ``gossamer'' correlation tails raises concerns about their ability to accurately describe bulk gaps. Here, we address this challenge and demonstrate that PEPS can reliably characterize gapped bulk excitations in chiral topological phases. Using a variational principle for excited states within a local mode approximation, we establish that correlation functions decaying faster than r2r^{-2} are not necessarily related to gapless modes and thus long-range ``gossamer'' correlation tails in chiral PEPS do not contradict the presence of a bulk gap. This framework is validated in the spin-12\frac{1}{2} Kitaev model with a chiral term, where PEPS yields excitation gaps that agree well with exact solutions. Extending our approach to the Z3\mathbb{Z}_3 Kitaev model, we present compelling evidence for its chiral ground state and accurately resolve its gapped excitations. These findings thus solidify PEPS as a powerful tool for studying both ground and excited states in chiral topological systems, thereby bridging a key gap in the understanding of their bulk properties.

Local ergotropy dynamically witnesses many-body localized phases

Authors: Francesco Formicola, Grazia Di Bello, Giulio De Filippis, Vittorio Cataudella, Donato Farina, Carmine Antonio Perroni

arXiv ID: 2502.20002 | Date: 2025-02-27

Abstract: Many-body localization is a dynamical phenomenon characteristic of strongly interacting and disordered many-body quantum systems which fail to achieve thermal equilibrium. From a quantum information perspective, the fingerprint of this phenomenon is the logarithmic growth of the entanglement entropy over time. We perform intensive numerical simulations, applied to a paradigmatic model system, showing that the local ergotropy, the maximum extractable work via local unitary operations on a small subsystem in the presence of Hamiltonian coupling, dynamically witnesses the change from ergodic to localized phases. Within the many-body localized phase, both the local ergotropy and its quantum fluctuations slowly vary over time with a characteristic logarithmic law analogous to the behaviour of entanglement entropy. This showcases how directly leveraging local control, instead of local observables or entropies analyzed in previous works, provides a thermodynamic marker of localization phenomena based on the locally extractable work.

Frobenius subalgebra lattices in tensor categories

Authors: Mainak Ghosh, Sebastien Palcoux

arXiv ID: 2502.19876 | Date: 2025-02-27

Abstract: This paper studies Frobenius subalgebra posets in abelian monoidal categories and shows that, under general conditions--satisfied in all semisimple tensor categories over the complex field--they collapse to lattices through a rigidity invariance perspective. Based on this, we extend Watatani's finiteness theorem for intermediate subfactors by proving that, under a weak positivity assumption--met by all semisimple tensor categories over the complex field--and a compatibility condition--fulfilled by all pivotal ones--the lattices arising from connected Frobenius algebras are finite. We also derive a non-semisimple version via semisimplification. Our approach relies on the concept of a formal angle, and the extension of key results--such as the planar algebraic exchange relation and Landau's theorems--to linear monoidal categories. Major applications of our findings include a stronger version of the Ino-Watatani result: we show that the finiteness of intermediate C*-algebras holds in a finite-index unital irreducible inclusion of C*-algebras without requiring the simple assumption. Moreover, for a finite-dimensional semisimple Hopf algebra H, we prove that H* is a Frobenius algebra object in Rep(H) and has a finite number of rigid invariant Frobenius subalgebras. Finally, we explore a range of applications, including abstract spin chains, vertex operator algebras and speculations on quantum arithmetic involving the generalization of Ore's theorem, Euler's totient and sigma functions, and RH.

Quantitative Description of Strongly Correlated Materials by Combining Downfolding Techniques and Tensor Networks

Authors: Daan Vrancken, Simon Ganne, Daan Verraes, Tom Braeckevelt, Lukas Devos, Laurens Vanderstraeten, Jutho Haegeman, Veronique Van Speybroeck

arXiv ID: 2502.19588 | Date: 2025-02-26

Abstract: We present a high-accuracy procedure for electronic structure calculations of strongly correlated materials. To address limitations in current electronic structure methods, we employ density functional theory in combination with the constrained random phase approximation to construct an effective multi-band Hubbard model, which is subsequently solved using tensor networks. Our work focuses on one-dimensional and quasi-one-dimensional materials, for which we employ the machinery of matrix product states. We apply this framework to the conjugated polymers trans-polyacetylene and polythiophene, as well as the quasi-one-dimensional charge-transfer insulator Sr2CuO3. The predicted band gaps show quantitative agreement with state-of-the-art computational techniques and experimental measurements. Beyond band gaps, tensor networks provide access to a wide range of physically relevant properties, including spin magnetization and various excitation energies. Their flexibility supports the implementation of complex Hamiltonians with longer-range interactions, while the bond dimension enables systematic control over accuracy. Furthermore, the computational cost scales efficiently with system size, demonstrating the framework's scalability.

Inexact subspace projection methods for low-rank tensor eigenvalue problems

Authors: Alec Dektor, Peter DelMastro, Erika Ye, Roel Van Beeumen, Chao Yang

arXiv ID: 2502.19578 | Date: 2025-02-26

Abstract: We propose inexact subspace iteration for solving high-dimensional eigenvalue problems with low-rank structure. Inexactness stems from low-rank compression, enabling efficient representation of high-dimensional vectors in a low-rank tensor format. A primary challenge in these methods is that standard operations, such as matrix-vector products and linear combinations, increase tensor rank, necessitating rank truncation and hence approximation. We compare the proposed methods with an existing inexact Lanczos method with low-rank compression. This method constructs an approximate orthonormal Krylov basis, which is often difficult to represent accurately in low-rank tensor formats, even when the eigenvectors themselves exhibit low-rank structure. In contrast, inexact subspace iteration uses approximate eigenvectors (Ritz vectors) directly as a subspace basis, bypassing the need for an orthonormal Krylov basis. Our analysis and numerical experiments demonstrate that inexact subspace iteration is much more robust to rank-truncation errors compared to the inexact Lanczos method. We also demonstrate that rank-truncated subspace iteration can converge for problems where the DMRG method stagnates. Furthermore, the proposed subspace iteration methods do not require a Hermitian matrix, in contrast to Lanczos and DMRG, which are designed specifically for Hermitian matrices.

An Analysis of First- and Quasi-Second-Order Optimization Algorithms in Variational Monte Carlo

Authors: Ruojing Peng, Garnet Kin-Lic Chan

arXiv ID: 2502.19576 | Date: 2025-02-26

Abstract: Many quantum many-body wavefunctions, such as Jastrow-Slater, tensor network, and neural quantum states, are studied with the variational Monte Carlo technique, where stochastic optimization is usually performed to obtain a faithful approximation to the ground-state of a given Hamiltonian. While first-order gradient descent methods are commonly used for such optimizations, quasi-second-order optimization formulations offer the potential of faster convergence under certain theoretical conditions, but with a similar cost per sample to first-order methods. However, the relative performance of first-order and second-order optimizers is influenced in practice by many factors, including the sampling requirements for a faithful optimization step, the influence of wavefunction quality, as well as the wavefunction parametrization and expressivity. Here we analyze these performance characteristics of first-order and quasi-second-order optimization methods for a variety of Hamiltonians, with the additional context of understanding the scaling of these methods (for good performance) as a function of system size. Our findings help clarify the role of first-order and quasi-second-order methods in variational Monte Carlo calculations and the conditions under which they should respectively be used. In particular, we find that unlike in deterministic optimization, where closeness to the variational minimum determines the suitability of second-order methods, in stochastic optimization the main factor is the overall expressivity of the wavefunction: quasi-second-order methods lead to an overall reduction in cost relative to first-order methods when the wavefunction is sufficiently expressive to represent the ground-state, even when starting far away from the ground state. This makes quasi-second-order methods an important technique when used with wavefunctions with arbitrarily improvable accuracy.

Long-range nonstabilizerness and phases of matter

Authors: David Aram Korbany, Michael J. Gullans, Lorenzo Piroli

arXiv ID: 2502.19504 | Date: 2025-02-26

Abstract: Long-range nonstabilizerness can be defined as the amount of nonstabilizerness which cannot be removed by shallow local quantum circuits. In this work, we study long-range nonstabilizerness in the context of many-body quantum physics, a task with possible implications for quantum-state preparation protocols and implementation of quantum-error correcting codes. After presenting a simple argument showing that long-range nonstabilizerness is a generic property of many-body states, we restrict to the class of ground states of gapped local Hamiltonians. We focus on one-dimensional systems and present rigorous results in the context of translation-invariant matrix product states (MPSs). By analyzing the fixed points of the MPS renormalization-group flow, we provide a sufficient condition for long-range nonstabilizerness, which depends entirely on the local MPS tensors. Physically, our condition captures the fact that the mutual information between distant regions of stabilizer fixed points is quantized, and this fact is not changed after applying shallow quantum circuits. We also discuss possible ramifications in the classification of phases of matter and quantum error correction.

Probing Green's Function Zeros by Co-tunneling through Mott Insulators

Authors: Carl Lehmann, Lorenzo Crippa, Giorgio Sangiovanni, Jan Carl Budich

arXiv ID: 2502.19479 | Date: 2025-02-26

Abstract: Quantum tunneling experiments have provided deep insights into basic excitations occurring as Green's function poles in the realm of complex quantum matter. However, strongly correlated quantum materials also allow for Green's functions zeros (GFZ) that may be seen as an antidote to the familiar poles, and have so far largely eluded direct experimental study. Here, we propose and investigate theoretically how co-tunneling through Mott insulators enables direct access to the shadow band structure of GFZ. In particular, we derive an effective Hamiltonian for the GFZ that is shown to govern the co-tunneling amplitude and reveal fingerprints of many-body correlations clearly distinguishing the GFZ structure from the underlying free Bloch band structure of the system. Our perturbative analytical results are corroborated by numerical data both in the framework of exact diagonalization and matrix product state simulations for a one-dimensional model system consisting of a Su-Schrieffer-Heeger-Hubbard model coupled to two single level quantum dots.

Dynamical cluster-based strategy for improving tensor network algorithms in quantum circuit simulations

Authors: Andrea De Girolamo, Paolo Facchi, Peter Rabl, Saverio Pascazio, Cosmo Lupo, Giuseppe Magnifico

arXiv ID: 2502.19289 | Date: 2025-02-26

Abstract: We optimize matrix-product state-based algorithms for simulating quantum circuits with finite fidelity, specifically the time-evolving block decimation (TEBD) and the density-matrix renormalization group (DMRG) algorithms, by exploiting the irregular arrangement of entangling operations in circuits. We introduce a variation of the standard TEBD algorithm, we termed "cluster-TEBD", which dynamically arranges qubits into entanglement clusters, enabling the exact contraction of multiple circuit layers in a single time step. Moreover, we enhance the DMRG algorithm by introducing an adaptive protocol, which analyzes the entanglement distribution within each circuit section to be contracted, dynamically adjusting the qubit grouping at each iteration. We analyze the performances of these enhanced algorithms in simulating both stabilizer and nonstabilizer random-structured quantum circuits, with up to 1000 qubits and 100 layers of Clifford and non-Clifford gates, and in simulating Shor's quantum algorithm with up to hundreds of thousands of layers. Our findings show that, even with reasonable computational resources per task, cluster-based approaches can significantly speed up simulations of large-sized quantum circuits and improve the fidelity of the final states.

Oddities in the Entanglement Scaling of the Quantum Six-Vertex Model

Authors: Sunny Pradhan, Jesús Cobos, Enrique Rico, Germán Sierra

arXiv ID: 2502.19152 | Date: 2025-02-26

Abstract: We investigate the entanglement properties of the Quantum Six-Vertex Model on a cylinder, focusing on the Shannon-Renyi entropy in the limit of Renyi order n=n = \infty. This entropy, calculated from the ground state amplitudes of the equivalent XXZ spin-1/2 chain, allows us to determine the Renyi entanglement entropy of the corresponding Rokhsar-Kivelson wavefunctions, which describe the ground states of certain conformal quantum critical points. Our analysis reveals a novel logarithmic correction to the expected entanglement scaling when the system size is odd. This anomaly arises from the geometric frustration of spin configurations imposed by periodic boundary conditions on odd-sized chains. We demonstrate that the scaling prefactor of this logarithmic term is directly related to the compactification radius of the low-energy bosonic field theory description, or equivalently, the Luttinger parameter. Thus, this correction provides a direct probe of the underlying Conformal Field Theory (CFT) describing the critical point. Our findings highlight the crucial role of system size parity in determining the entanglement properties of this model and offer insights into the interplay between geometry, frustration, and criticality.

Theory of interaction-induced charge order in CrSBr

Authors: Zhi-Hao Cui, Andrew J. Millis, David R. Reichman

arXiv ID: 2502.18649 | Date: 2025-02-25

Abstract: CrSBr is a layered van der Waals insulator with a quasi one-dimensional electronic structure and in-plane ferromagnetic order. Recent experimental work on Li-doped CrSBr reveals quasi-1D charge modulated states. In this study, we develop ab initio effective models for CrSBr to investigate these states and solve them using mean-field theory and density matrix embedding theory. The models are parametrized using density functional theory, the constrained random phase approximation, and the Rytova-Keldysh form of the long-range Coulomb interaction. Our simulations indicate the emergence of a charge density wave state characterized by cosine-like intra-chain density modulations and inter-chain phase shifts that minimize the Coulomb repulsion. Notably, at a doping level corresponding to 1/n1/n electron per CrSBr unit, the most stable pattern exhibits a periodicity of nn cells, in agreement with experimental observations and Peierls' instability arguments. Moreover, we demonstrate that the inter-chain order is sensitive to the range of Coulomb interactions. If the interaction is hard-truncated to a short-ranged form, some localized stripe-like states are computationally favored. This work provides an ab initio framework for understanding the interplay of competing electronic and magnetic phases in CrSBr and related materials.

Optimal Symbolic Construction of Matrix Product Operators and Tree Tensor Network Operators

Authors: Hazar Çakır, Richard M. Milbradt, Christian B. Mendl

arXiv ID: 2502.18630 | Date: 2025-02-25

Abstract: This research introduces an improved framework for constructing matrix product operators (MPOs) and tree tensor network operators (TTNOs), crucial tools in quantum simulations. A given (Hamiltonian) operator typically has a known symbolic "sum of operator strings" form that can be translated into a tensor network structure. Combining the existing bipartite-graph-based approach and a newly introduced symbolic Gaussian elimination preprocessing step, our proposed method improves upon earlier algorithms in cases when Hamiltonian terms share the same prefactors. We test the performance of our method against established ones for benchmarking purposes. Finally, we apply our methodology to the model of a cavity filled with molecules in a solvent. This open quantum system is cast into the hierarchical equation of motion (HEOM) setting to obtain an effective Hamiltonian. Construction of the corresponding TTNO demonstrates a sub-linear increase of the maximum bond dimension.

Berezinskii-Kosterlitz-Thouless Renormalization Group Flow at a Quantum Phase Transition

Authors: Matthias Thamm, Harini Radhakrishnan, Hatem Barghathi, C. M. Herdman, Arpan Biswas, Bernd Rosenow, Adrian Del Maestro

arXiv ID: 2502.18622 | Date: 2025-02-25

Abstract: We present a controlled numerical study of the Berezinskii-Kosterlitz-Thouless (BKT) transition in the one-dimensional Bose-Hubbard model at unit filling, providing evidence of the characteristic logarithmic finite-size scaling of the BKT transition. Employing density matrix renormalization group and quantum Monte Carlo simulations under periodic boundary conditions, together with a systematic finite-size scaling analysis of bipartite particle number fluctuations, we resolve boundary-induced complications that previously obscured critical scaling. We demonstrate that a suitably chosen central region under open boundaries reproduces universal RG signatures, reconciling earlier discrepancies. Finally, leveraging a non-parametric Bayesian analysis, we determine the critical interaction strength with high precision, establishing a benchmark for BKT physics in one-dimensional quantum models.

Entanglement transitions in a boundary-driven open quantum many-body system

Authors: Darvin Wanisch, Nora Reinić, Daniel Jaschke, Simone Montangero, Pietro Silvi

arXiv ID: 2502.18372 | Date: 2025-02-25

Abstract: We introduce a numerical framework for integrating Markovian dynamics on tree tensor operator (TTO) ansatz states. This framework enables the simulation of both transient and steady-state regimes of systems governed by the Lindblad master equation, while preserving positivity of the density matrix and providing direct access to entanglement monotones. We demonstrate its capability to probe entanglement in open quantum many-body systems and to distinguish it from other correlations by studying a boundary-driven XXZ spin chain. Our analysis uncovers entanglement transitions driven by both the coupling to the environment and the anisotropy, revealing a striking connection between spatial entanglement scaling and spin-current.

Quantum entanglement of fermionic symmetry-enriched quantum critical points in one dimension

Authors: Wen-Hao Zhong, Hai-Qing Lin, Xue-Jia Yu

arXiv ID: 2502.18178 | Date: 2025-02-25

Abstract: Quantum entanglement can be an effective diagnostic tool for probing topological phases protected by global symmetries. Recently, the notion of nontrivial topology in critical systems has been proposed and is attracting growing attention. In this work, as a concrete example, we explore the quantum entanglement properties of fermionic symmetry-enriched quantum critical points by constructing exactly solvable models based on stacked multiple Kitaev chains. We first analytically establish the global phase diagram using entanglement entropy and reveal three topologically distinct gapped phases with different winding numbers, along with three topologically distinct transition lines separating them. Importantly, we unambiguously demonstrate that two transition lines exhibit fundamentally different topological properties despite sharing the same central charge. Specifically, they display nontrivial topological degeneracy in the entanglement spectrum under periodic boundary conditions, thereby generalizing the Li-Haldane bulk-boundary correspondence to a broader class of fermionic symmetry-enriched criticality. Additionally, we identify a novel Lifshitz multicritical point at the intersection of the three transition lines, which also exhibits nontrivial topological degeneracy. This work provides a valuable reference for investigating gapless topological phases of matter from the perspective of quantum entanglement.

Model-Free Adversarial Purification via Coarse-To-Fine Tensor Network Representation

Authors: Guang Lin, Duc Thien Nguyen, Zerui Tao, Konstantinos Slavakis, Toshihisa Tanaka, Qibin Zhao

arXiv ID: 2502.17972 | Date: 2025-02-25

Abstract: Deep neural networks are known to be vulnerable to well-designed adversarial attacks. Although numerous defense strategies have been proposed, many are tailored to the specific attacks or tasks and often fail to generalize across diverse scenarios. In this paper, we propose Tensor Network Purification (TNP), a novel model-free adversarial purification method by a specially designed tensor network decomposition algorithm. TNP depends neither on the pre-trained generative model nor the specific dataset, resulting in strong robustness across diverse adversarial scenarios. To this end, the key challenge lies in relaxing Gaussian-noise assumptions of classical decompositions and accommodating the unknown distribution of adversarial perturbations. Unlike the low-rank representation of classical decompositions, TNP aims to reconstruct the unobserved clean examples from an adversarial example. Specifically, TNP leverages progressive downsampling and introduces a novel adversarial optimization objective to address the challenge of minimizing reconstruction error but without inadvertently restoring adversarial perturbations. Extensive experiments conducted on CIFAR-10, CIFAR-100, and ImageNet demonstrate that our method generalizes effectively across various norm threats, attack types, and tasks, providing a versatile and promising adversarial purification technique.

Using Matrix-Free Tensor-Network Optimizations to Construct a Reduced-Scaling and Robust Second-Order Møller-Plesset Theory

Authors: Karl Pierce, Miguel Morales

arXiv ID: 2502.17683 | Date: 2025-02-24

Abstract: We investigate the efficient combination of the canonical polyadic decomposition (CPD) and tensor hyper-contraction (THC) approaches. We first present a novel low-cost CPD solver which leverages a precomputed THC factorization of an order-44 tensor to efficiently optimize the order-44 CPD with O(NR2)\mathcal{O}(NR^2) scaling. With the matrix-free THC-based optimization strategy in hand we can: efficiently generate CPD factorizations of the order-4 two-electron integral tensors; and develop novel electronic structure methods which take advantage of both the THC and CPD approximations. Next, we investigate the application of a combined CPD and THC approximation of the Laplace transform (LT) second-order Møller-Plesset (MP2) method. We exploit the ability to switch efficiently between the THC and CPD factorizations of the two electron integrals to reduce the computational complexity of the LT MP2 method while preserving the accuracy of the approach. Furthermore we take advantage of the robust fitting approximation to eliminate leading order error in the CPD approximated tensor networks. Finally, we show that modest values of THC and CPD rank preserve the accuracy of the LT MP2 method and that this CPD+THC LT MP2 strategy realizes a performance advantage over canonical LT MP2 in both computational wall-times and memory resource requirements.

Real-time simulation of jet energy loss and entropy production in high-energy scattering with matter

Authors: João Barata, Enrique Rico

arXiv ID: 2502.17558 | Date: 2025-02-24

Abstract: In analogy to high-energy nuclear scattering experiments, we study a real-time scattering process between a propagating state and a dense target in 1+11+1-d massive QED. In our setup, we identify three distinct regimes that qualitatively characterize the evolution: for a dilute medium, the incoming probe state evolves nearly ballistically; in an intermediate setting, it traverses the matter, locally exciting it; and for dense targets, one approaches a black-disk limit, where the matter acts as a strong wall potential. We find evidence that the probe's energy loss rate scales linearly with the path length in the medium, and we study how the entanglement entropy reveals the mixing between the probe and medium states. With the goal of one day replicating high-energy nuclear experiments in quantum devices, we briefly discuss how the current tensor network-based simulations can be translated to a quantum simulator.

Phase coherence of charge-6e6e superconductors via a frustrated Kagome XY antiferromagnet

Authors: Feng-Feng Song, Guang-Ming Zhang

arXiv ID: 2502.17005 | Date: 2025-02-24

Abstract: Recent experimental evidence for the charge-6e6e condensed phase in kagome superconductors has generated significant interest. We investigate the unconventional superconductivity in the kagome superconductor CsV3Sb5\mathrm{CsV_3Sb_5}, focusing on the emergence of charge-6e6e superconductivity (SC) at temperatures higher than the conventional charge-2e2e SC state. By modeling the phase coherence of the SC order parameter using a frustrated antiferromagnetic XY model on an emergent kagome lattice, we show that the condensation of fractional vortices with 1/31/3 vorticity stabilizes phase coherence in exp(i3θ)\exp(i3θ), giving rise to the charge-6e6e SC state. Using a tensor network approach tailored for frustrated spin systems, we identify a Berezinskii-Kosterlitz-Thouless transition at Tc/J0.075T_c/J \simeq 0.075, where the unbinding of 1/31/3 fractional vortex-antivortex pairs transforms the system from the charge-6e6e SC phase to the normal phase. Below TcT_c, the 1/31/3 fractional vortex correlations exhibit power-law decay, while the integer vortex correlations decay exponentially, reflecting the dominance of charge-6e6e SC in the absence of charge-2e2e SC. Our results provide a theoretical understanding of the charge-6e6e SC in two-dimensional kagome superconductors, emphasizing the interplay between fractional vortices, frustration, and topology in stabilizing this exotic SC phase.

Spin-charge Kondo effect for a quantum dot with side coupled Majorana zero mode

Authors: Haojie Shen, Wei Su, Mengnan Chen, Xiaoqun Wang

arXiv ID: 2502.16640 | Date: 2025-02-23

Abstract: We investigate a minimal system consisting of a quantum dot coupled to a Majorana zero mode and a normal lead. We identify the underlying screening process as a novel spin-charge Kondo effect, where the low-energy spin and charge degrees of freedom of the Majorana zero mode-quantum dot subsystem are fully screened by those in the normal lead, resulting in the formation of a spin-charge singlet. An effective low-energy model is derived, with charge fluctuations appropriately accounted for. This spin-charge Kondo effect is found to be consistent with the spin-dependent Andreev/normal boundary conditions induced by the Majorana zero mode. We demonstrate that the anomalous substructure in the spectrum and thermodynamic properties is closely tied to the proportion of the charge component in the screening cloud. The spin-charge screening cloud exhibits scaling behavior analogous to that of traditional Kondo systems, though the sub-leading even-odd effect is subtly modified by the boundary conditions. These findings enhance our understanding of Kondo physics and resolve key debates on quantum dot nanostructures with Majorana zero modes.

Quantum Encoding of Structured Data with Matrix Product States

Authors: Josh Green, Jingbo B Wang

arXiv ID: 2502.16464 | Date: 2025-02-23

Abstract: The amplitude encoding of an arbitrary nn-qubit state vector requires Ω(2n)Ω(2^n) gate operations, owing to the exponential dimension of the Hilbert space. We can, however, form dimensionality-reduced representations of quantum states using matrix product states (MPS). In this article, we illustrate that MPS techniques enable the preparation of quantum states representative of functions with complexity up to low-degree piecewise polynomials via shallow-depth quantum circuits with accuracy exceeding 99.99\%. We extend these results to the approximate amplitude encoding of pixel values. We showcase this approach by efficiently preparing a 128×128128\times 128 ChestMNIST medical image (https://medmnist.com/) on 14 qubits with fidelity exceeding 99.2\% on a circuit with a total depth of just 425 single-qubit rotation and CNOT gates.

A comprehensive study of out-of-equilibrium Kondo effect and Coulomb blockade

Authors: Matthieu Jeannin, Yuriel Núñez-Fernández, Thomas Kloss, Olivier Parcollet, Xavier Waintal

arXiv ID: 2502.16306 | Date: 2025-02-22

Abstract: We present a comprehensive set of numerically exact results for the Anderson model of a quantum dot coupled to two electrodes in non-equilibrium regime. We use a high order perturbative expansion in power of the interaction UU, coupled to a cross-extrapolation method to long time and large interaction. The perturbative series is computed up to 202520-25 orders, using tensor cross-interpolation. We calculate the full Coulomb diamond bias voltage - gate voltage map, including its Kondo ridge, that forms the standard experimental signature of the Coulomb blockage and the Kondo effect. We present current-voltage characteristics that spans three orders of magnitude in bias voltage and display five different regimes of interest from probing the Kondo resonance at small bias to saturation at very high bias. Our technique also naturally produces time-resolved interaction quenches which we use to study the dynamics of the formation of the Kondo cloud. Finally, we predict several qualitatively new physical features that should be within reach of existing or upcoming experiments.

Entanglement corner dependence in two-dimensional systems: A tensor network perspective

Authors: Noa Feldman, Moshe Goldstein

arXiv ID: 2502.15467 | Date: 2025-02-21

Abstract: In continuous quantum field theories, the entanglement entropy of a subsystem with sharp corners in its boundary exhibits a universal corner-dependent contribution. We study this contribution via the lens of discretized systems, and demonstrate that this corner dependence emerges naturally from the geometric structure of infinite projected entangled pair states (iPEPS) on discrete lattices. Using a rigorous counting argument, we show that the bond dimension of an iPEPS representation exhibits a corner-dependent term that matches the predicted term in gapped continuous systems. Crucially, we find that this correspondence only emerges when averaging over all possible lattice orientations, revealing a fundamental requirement for properly discretizing continuous systems. Our results provide a geometric understanding of entanglement corner laws and establish a direct connection between analytical field theory predictions and the structure of tensor network representations. We extend our analysis to gauge-invariant systems, where lattice corners crossed by the bipartition boundary contribute an additional corner-dependent term. These findings offer new insights into the relationship between entanglement in continuous and discrete quantum systems.

Optimization of path-integral tensor-multiplication schemes in open quantum systems

Authors: L. M. J. Hall, A. Gisdakis, E. A. Muljarov

arXiv ID: 2502.15136 | Date: 2025-02-21

Abstract: Path-integral techniques are a powerful tool used in open quantum systems to provide an exact solution for the non-Markovian dynamics. However, the exponential scaling of the tensor size with quantum memory length of these techniques limits the applicability when applied to systems with long memory times. Here we provide a general optimization of tensor multiplication schemes for systems with pair correlations and finite memory times. This optimization effectively reduces the tensor sizes by using a matrix representation of tensors combined with singular value decomposition to filter out negligible contributions. This approach dramatically reduces both computational time and memory usage of the traditional tensor-multiplication schemes. Calculations that would require over 50 million GB of RAM in the original approach are now available on standard computers, allowing access to new regimes and more complex systems. While more memory-efficient representations exist, this approach enables an extrapolation scheme that other techniques do not offer. As a demonstration, we apply it to the Trotter decomposition with linked cluster expansion technique, and use it to investigate a quantum dot-microcavity system at larger coupling strengths than previously achieved. We also apply the optimization in a case where the memory time is very long -- specifically in a system containing two spatially separated quantum dots in a common phonon bath.

Digitized counterdiabatic quantum critical dynamics

Authors: Anne-Maria Visuri, Alejandro Gomez Cadavid, Balaganchi A. Bhargava, Sebastián V. Romero, András Grabarits, Pranav Chandarana, Enrique Solano, Adolfo del Campo, Narendra N. Hegade

arXiv ID: 2502.15100 | Date: 2025-02-20

Abstract: We experimentally demonstrate that a digitized counterdiabatic quantum protocol reduces the number of topological defects created during a fast quench across a quantum phase transition. To show this, we perform quantum simulations of one- and two-dimensional transverse-field Ising models driven from the paramagnetic to the ferromagnetic phase. We utilize superconducting cloud-based quantum processors with up to 156 qubits. Our data reveal that the digitized counterdiabatic protocol reduces defect formation by up to 48% in the fast-quench regime -- an improvement hard to achieve through digitized quantum annealing under current noise levels. The experimental results closely match theoretical and numerical predictions at short evolution times, before deviating at longer times due to hardware noise. In one dimension, we derive an analytic solution for the defect number distribution in the fast-quench limit. For two-dimensional geometries, where analytical solutions are unknown and numerical simulations are challenging, we use advanced matrix-product-state methods. Our findings indicate a practical way to control the topological defect formation during fast quenches and highlight the utility of counterdiabatic protocols for quantum optimization and quantum simulation in material design on current quantum processors.

Incommensurate gapless ferromagnetism connecting competing symmetry-enriched deconfined quantum phase transitions

Authors: Anthony Rey, Ömer M. Aksoy, Daniel P. Arovas, Claudio Chamon, Christopher Mudry

arXiv ID: 2502.14958 | Date: 2025-02-20

Abstract: We present a scenario, in which a gapless extended phase serves as a "hub" connecting multiple symmetry-enriched deconfined quantum critical points. As a concrete example, we construct a lattice model with Z2×Z2×Z2\mathbb{Z}^{\,}_{2}\times \mathbb{Z}^{\,}_{2}\times \mathbb{Z}^{\,}_{2} symmetry for quantum spin-1/2 degrees of freedom that realizes four distinct gapful phases supporting antiferromagnetic long-range order and one extended incommensurate gapless ferromagnetic phase. The quantum phase transition between any two of the four gapped and antiferromagnetic phases goes through either a (deconfined) quantum critical point, a quantum tricritical point, or the incommensurate gapless ferromagnetic phase. In this phase diagram, it is possible to interpolate between four deconfined quantum critical points by passing through the extended gapless ferromagnetic phase. We identify the phases in the model and the nature of the transitions between them through a combination of analytical arguments and density matrix renormalization group studies.

Emergent Goldstone flat bands and spontaneous symmetry breaking with type-B Goldstone modes

Authors: Huan-Qiang Zhou, Jesse J. Osborne, Qian-Qian Shi, Ian P. McCulloch

arXiv ID: 2502.14605 | Date: 2025-02-20

Abstract: For a quantum many-body spin system undergoing spontaneous symmetry breaking with type-B Goldstone modes, a high degree of degeneracy arises in the ground state manifold. Generically, if this degeneracy is polynomial in system size, then it does not depend on the type of boundary conditions used. However, if there exists an emergent (local) symmetry operation tailored to a specific degenerate ground state, then we show that the degeneracies are exponential in system size and are different under periodic boundary conditions (PBCs) and open boundary conditions (OBCs). We further show that the exponential ground state degeneracies in turn imply the emergence of Goldstone flat bands -- single-mode excitations generated by a multi-site operator and its images under the repeated action of the translation operation under PBCs or the cyclic permutation symmetry operation under OBCs. Conversely, we also show that the presence of emergent Goldstone flat bands implies that there exists an emergent (local) symmetry operation tailored to a specific degenerate ground state. In addition, we propose an extrinsic characterization of emergent Goldstone flat bands, revealing a connection to quantum many-body scars, which violate the eigenstate thermalization hypothesis. We illustrate this by presenting examples from the staggered SU(4){\rm SU}(4) spin-1 ferromagnetic biquadratic model and the staggered SU(4){\rm SU}(4) ferromagnetic spin-orbital model. We also perform extensive numerical simulations for the more general SO(3){\rm SO}(3) spin-1 bilinear-biquadratic and SO(4){\rm SO(4)} ferromagnetic spin-orbital models, containing the two aforementioned models as the endpoints in the ferromagnetic regimes respectively, and confirm the emergence of Goldstone flat bands, as we approach these endpoints from deep inside the ferromagnetic regimes.

Topological phase transition through tunable nearest-neighbor interactions in a one-dimensional lattice

Authors: Rajashri Parida, Diptiman Sen, Tapan Mishra

arXiv ID: 2502.14603 | Date: 2025-02-20

Abstract: We investigate the phase diagram of a one-dimensional model of hardcore bosons or spinless fermions with tunable nearest-neighbor interactions. By introducing alternating repulsive and attractive interactions on consecutive bonds, we show that the system undergoes a transition from a bond-ordered (BO) phase to a charge-density wave-II (CDW-II) phase as the attractive interaction strength increases at a fixed repulsive interaction. For a specific interaction pattern, the BO phase exhibits topological properties, which vanish when the pattern is altered, leading to a transition from a topological BO phase to a trivial BO phase through a gap-closing point where both interactions vanish. We identify these phases using a combination of order parameters, topological invariants, edge-state analysis and Thouless charge pumping. By extending our analysis beyond half-filling, we explore the phase diagram across all densities and identify the superfluid (SF) and the pair-superfluid (PSF) phases, characterized by single-particle and bound-pair excitations at incommensurate densities. The proposed model is experimentally realizable in platforms such as Rydberg excited or ultracold atoms in optical lattices, offering a versatile framework to study such interplay between topology and interactions in low-dimensional systems.

Exploring the phase diagram of SU(2)4SU(2)_4 strange correlator

Authors: Ce Shen

arXiv ID: 2502.14556 | Date: 2025-02-20

Abstract: We investigate the phase diagram of a quantum many-body system constructed via the strange correlator approach, based on the non-Abelian SU(2)4SU(2)_4 fusion category, to probe topological phase transitions. Using tensor network methods, we numerically compute the half-infinite chain entanglement entropy derived from the dominant eigenvector of the transfer matrix and map the entropy across a spherical two-dimensional parameter space. Our results reveal a phase diagram significantly more complex than previously reported, including a gapless phase consistent with a conformal field theory (CFT) of central charge c=1c=1. Critical lines separating distinct phases are identified, with one such line bounding the CFT phase exhibiting a higher central charge c=2c=2, indicative of an unconventional critical regime.

Monomer-dimer tensor-network basis for qubit-regularized lattice gauge theories

Authors: Shailesh Chandrasekharan, Rui Xian Siew, Tanmoy Bhattacharya

arXiv ID: 2502.14175 | Date: 2025-02-20

Abstract: Traditional SU(N)\mathrm{SU}(N) lattice gauge theories (LGTs) can be formulated using an orthonormal basis constructed from the irreducible representations (irreps) VλV_λ of the SU(N)\mathrm{SU}(N) gauge symmetry. On a lattice, the elements of this basis are tensor networks comprising dimer tensors on the links labeled by a set of irreps {λ}\{λ_\ell\} and monomer tensors on sites labeled by {λs}\{λ_s\}. These tensors naturally define a local site Hilbert space, Hsg\mathcal{H}^g_s, on which gauge transformations act. Gauss's law introduces an additional index αs=1,2,,D(Hsg)α_s = 1, 2, \dots, \mathcal{D}(\mathcal{H}_s^g) that labels an orthonormal basis of the gauge-invariant subspace of Hsg\mathcal{H}^g_s. This monomer-dimer tensor-network (MDTN) basis, {λs},{λ},{αs}\left| \{λ_s\},\{λ_\ell\},\{α_s\}\right\rangle, of the physical Hilbert space enables the construction of new qubit-regularized SU(N)\mathrm{SU}(N) gauge theories that are free of sign problems while preserving key features of traditional LGTs. Here, we investigate finite-temperature confinement-deconfinement transitions in a simple qubit-regularized SU(2)\mathrm{SU}(2) and SU(3)\mathrm{SU}(3) gauge theory in d=2d=2 and d=3d=3 spatial dimensions, formulated using the MDTN basis, and show that they reproduce the universal results of traditional LGTs at these transitions. Additionally, in d=1d=1, we demonstrate using a plaquette chain that the string tension at zero temperature can be continuously tuned to zero by adjusting a model parameter that plays the role of the gauge coupling in traditional LGTs.

Quantum spin liquid phase in the Shastry-Sutherland model revealed by high-precision infinite projected entangled-pair states

Authors: Philippe Corboz, Yining Zhang, Boris Ponsioen, Frédéric Mila

arXiv ID: 2502.14091 | Date: 2025-02-19

Abstract: The Shastry-Sutherland model is an effective model of the layered material SrCu2_2(BO3_3)2_2, which exhibits an extremely rich phase diagram as a function of pressure and magnetic field. Motivated by the recent controversy regarding its phase diagram at zero magnetic field, we perform large-scale simulations based on infinite projected entangled-pair states (iPEPS), a two-dimensional tensor network ansatz to represent the ground state directly in the thermodynamic limit. By employing the latest optimization techniques, we obtain variational states with lower energy than previous results obtained from other methods. Using systematic extrapolations to the exact infinite bond dimension limit, our simulations reveal a narrow quantum spin liquid phase between the plaquette and antiferromagnetic phases in the range 0.785(5)J/J0.82(1)0.785(5) \le J'/J \le 0.82(1).

Decoherence-induced self-dual criticality in topological states of matter

Authors: Qingyuan Wang, Romain Vasseur, Simon Trebst, Andreas W. W. Ludwig, Guo-Yi Zhu

arXiv ID: 2502.14034 | Date: 2025-02-19

Abstract: Quantum measurements can be employed to induce decoherence in a restricted segment of a larger quantum many-body state, while generating entanglement for its remaining constituents. We demonstrate generally that measurement-induced phase transitions can be viewed as decoherence-induced critical mixed states. In this context, a deeper conceptual understanding is called for with regard to symmetry as an organizing principle. Integrating these connections we investigate the role of self-dual symmetry in mixed states, showing that the decoherence of electric (e) and magnetic (m) vortices from the 2D bulk of the toric code, or equivalently, a 2D cluster state with symmetry-protected topological order, can leave a (1+1)D quantum critical mixed state on the boundary protected by a weak Kramers-Wannier self-dual symmetry. The corresponding self-dual critical bulk is described by the N1N\to1 limit of the 2D Non-linear Sigma Model in symmetry class D with target space SO(2N)/U(N) at ΘΘ-angle ππ, and represents a "measurement-version" of the Cho-Fisher network model subjected to Born-rule randomness. Explicit breaking of self-duality, by incoherent noise amounting to fermion interactions or (non-interacting) coherent deformation, is shown to induce an RG crossover from this self-dual critical state to Nishimori criticality or to it from a novel type of Ising+ criticality, respectively, both related to the random-bond Ising model in different replica limits. Using an unbiased numerical approach combining tensor network, Monte Carlo, and Gaussian fermion simulations, we chart out a global phase diagram as diagnosed by coherent information and entanglement entropy measures. Our results point to a way towards a general understanding of mixed-state criticality in open quantum systems in terms of symmetry and topology.

Extended ss-wave pairing from an emergent Feshbach resonance in bilayer nickelate superconductors

Authors: Pietro Borchia, Hannah Lange, Fabian Grusdt

arXiv ID: 2502.13960 | Date: 2025-02-19

Abstract: Since the discovery of unconventional superconductivity in cuprates, unraveling the pairing mechanism of charge carriers in doped antiferromagnets has been a long-standing challenge. Motivated by the discovery of high-Tc_c superconductivity in nickelate bilayer La3_3Ni2_2O7_7 (LNO), we study a minimal mixed dimensional (MixD) tJt-J model supplemented with a repulsive Coulomb interaction VV. When hole-doped, previous numerical simulations revealed that the system exhibits strong binding energies, with a phenomenology resembling a BCS-to-BEC crossover accompanied by a Feshbach resonance between two distinct types of charge carriers. Here, we perform a mean-field analysis that enables a direct observation of the BCS-to-BEC crossover as well as microscopic insights into the crossover region and the pairing symmetry for two-dimensional bilayers. We benchmark our mean-field description by comparing it to density-matrix renormalization group (DMRG) simulations in quasi-one dimensional settings and find remarkably good agreement. For the two-dimensional system relevant to LNO our mean-field calculations predict a BCS pairing gap with an extended ss-wave symmetry, directly resulting from the pairing mechanism's Feshbach-origin. Our analysis hence gives insights into pairing in unconventional superconductors and, further, can be tested in currently available ultracold atom experiments.

Correcting and extending Trotterized quantum many-body dynamics

Authors: Gian Gentinetta, Friederike Metz, Giuseppe Carleo

arXiv ID: 2502.13784 | Date: 2025-02-19

Abstract: A complex but important challenge in understanding quantum mechanical phenomena is the simulation of quantum many-body dynamics. Although quantum computers offer significant potential to accelerate these simulations, their practical application is currently limited by noise and restricted scalability. In this work, we address these problems by proposing a hybrid ansatz combining the strengths of quantum and classical computational methods. Using Trotterization, we evolve an initial state on the quantum computer according to a simplified Hamiltonian, focusing on terms that are difficult to simulate classically. A classical model then corrects the simulation by including the terms omitted in the quantum circuit. While the classical ansatz is optimized during the time evolution, the quantum circuit has no variational parameters. Derivatives can thus be calculated purely classically, avoiding challenges arising in the optimization of parameterized quantum circuits. We demonstrate three applications of this hybrid method. First, our approach allows us to avoid SWAP gates in the quantum circuit by restricting the quantum part of the ansatz to hardware-efficient terms of the Hamiltonian. Second, we can mitigate errors arising from the Trotterization of the time evolution unitary. Finally, we can extend the system size while keeping the number of qubits on the quantum device constant by including additional degrees of freedom in the classical ansatz.

Accurate Simulation of the Hubbard Model with Finite Fermionic Projected Entangled Pair States

Authors: Wen-Yuan Liu, Huanchen Zhai, Ruojing Peng, Zheng-Cheng Gu, Garnet Kin-Lic Chan

arXiv ID: 2502.13454 | Date: 2025-02-19

Abstract: We demonstrate the use of finite-size fermionic projected entangled pair states, in conjunction with variational Monte Carlo, to perform accurate simulations of the ground-state of the 2D Hubbard model. Using bond dimensions of up to D=28D=28, we show that we can surpass state-of-the-art DMRG energies that use up to m=32000m=32000 SU(2) multiplets on 8-leg ladders. We further apply our methodology to 10×1610\times 16, 12×1612\times 16 and 16×1616 \times 16 lattices at 1/81/8 hole doping and observe the dimensional crossover between stripe orientations. Our work shows the power of finite-size fermionic tensor networks to resolve the physics of the 2D Hubbard model and related problems.

Triangular lattice models of the Kalmeyer-Laughlin spin liquid from coupled wires

Authors: Tingyu Gao, Niklas Tausendpfund, Erik L. Weerda, Jan Naumann, Matteo Rizzi, David F. Mross

arXiv ID: 2502.13223 | Date: 2025-02-18

Abstract: Chiral spin liquids (CSLs) are exotic phases of interacting spins in two dimensions, characterized by long-range entanglement and fractional excitations. We construct a local Hamiltonian on the triangular lattice that stabilizes the Kalmeyer-Laughlin CSL without requiring fine-tuning. Our approach employs coupled-wire constructions and introduces a lattice duality to construct a solvable chiral sliding Luttinger liquid, which is driven toward the CSL phase by generic perturbations. By combining symmetry analysis and bosonization, we make sharp predictions for the ground states on quasi-one-dimensional cylinders and tori, which exhibit a fourfold periodicity in the circumference. Extensive tensor network simulations demonstrating ground-state degeneracies, fractional quasiparticles, nonvanishing long-range order parameters, and entanglement signatures confirm the emergence of the CSL in the lattice Hamiltonian.

tn4ml: Tensor Network Training and Customization for Machine Learning

Authors: Ema Puljak, Sergio Sanchez-Ramirez, Sergi Masot-Llima, Jofre Vallès-Muns, Artur Garcia-Saez, Maurizio Pierini

arXiv ID: 2502.13090 | Date: 2025-02-18

Abstract: Tensor Networks have emerged as a prominent alternative to neural networks for addressing Machine Learning challenges in foundational sciences, paving the way for their applications to real-life problems. This paper introduces tn4ml, a novel library designed to seamlessly integrate Tensor Networks into optimization pipelines for Machine Learning tasks. Inspired by existing Machine Learning frameworks, the library offers a user-friendly structure with modules for data embedding, objective function definition, and model training using diverse optimization strategies. We demonstrate its versatility through two examples: supervised learning on tabular data and unsupervised learning on an image dataset. Additionally, we analyze how customizing the parts of the Machine Learning pipeline for Tensor Networks influences performance metrics.

Predictive simulations of the dynamical response of mesoscopic devices

Authors: Samuel Boutin, Torsten Karzig, Tareq El Dandachi, Ryan V. Mishmash, Jan Gukelberger, Roman M. Lutchyn, Bela Bauer

arXiv ID: 2502.12960 | Date: 2025-02-18

Abstract: As the complexity of mesoscopic quantum devices increases, simulations are becoming an invaluable tool for understanding their behavior. This is especially true for the superconductor-semiconductor heterostructures used to build Majorana-based topological qubits, where quantitatively understanding the interplay of topological superconductivity, disorder, semiconductor quantum dots, Coulomb blockade and noise has been essential for progress on device design and interpretation of measurements. In this paper, we describe a general framework to simulate the low-energy quantum dynamics of such complex systems. We illustrate our approach by computing the dispersive gate sensing (DGS) response of quantum dots coupled to topological superconductors. We start by formulating the DGS response as an open-system quantum dynamics problem, which allows a consistent treatment of drive backaction as well as quantum and classical noise. For microscopic quantum problems subject to Coulomb-blockade, where a direct solution in the exponentially large many-body Hilbert space would be prohibitive, we introduce a series of controlled approximations that incorporate ideas from tensor network theory and quantum chemistry to reduce this Hilbert space to a few low-energy degrees of freedom that accurately capture the low-energy quantum dynamics. We demonstrate the methods introduced in this paper on the example of a single quantum dot coupled to a topological superconductor and a microscopic realization of the fermion parity readout setup of Aghaee et al. arXiv:2401.09549 (2024).

Tensor cross interpolation for global discrete optimization with application to Bayesian network inference

Authors: Sergey Dolgov, Dmitry Savostyanov

arXiv ID: 2502.12940 | Date: 2025-02-18

Abstract: Global discrete optimization is notoriously difficult due to the lack of gradient information and the curse of dimensionality, making exhaustive search infeasible. Tensor cross approximation is an efficient technique to approximate multivariate tensors (and discretized functions) by tensor product decompositions based on a small number of tensor elements, evaluated on adaptively selected fibers of the tensor, that intersect on submatrices of (nearly) maximum volume. The submatrices of maximum volume are empirically known to contain large elements, hence the entries selected for cross interpolation can also be good candidates for the globally maximal element within the tensor. In this paper we consider evolution of epidemics on networks, and infer the contact network from observations of network nodal states over time. By numerical experiments we demonstrate that the contact network can be inferred accurately by finding the global maximum of the likelihood using tensor cross interpolation. The proposed tensor product approach is flexible and can be applied to global discrete optimization for other problems, e.g. discrete hyperparameter tuning.

The Canonical Forms of Matrix Product States in Infinite-Dimensional Hilbert Spaces

Authors: Niilo Heikkinen

arXiv ID: 2502.12934 | Date: 2025-02-18

Abstract: In this work, we prove that any element in the tensor product of separable infinite-dimensional Hilbert spaces can be expressed as a matrix product state (MPS) of possibly infinite bond dimension. The proof is based on the singular value decomposition of compact operators and the connection between tensor products and Hilbert-Schmidt operators via the Schmidt decomposition in infinite-dimensional separable Hilbert spaces. The construction of infinite-dimensional MPS (idMPS) is analogous to the well-known finite-dimensional construction in terms of singular value decompositions of matrices. The infinite matrices in idMPS give rise to operators acting on (possibly infinite-dimensional) auxiliary Hilbert spaces. As an example we explicitly construct an MPS representation for certain eigenstates of a chain of three coupled harmonic oscillators.

Universality and emergent effective fluid from jets and string breaking in the massive Schwinger model using tensor networks

Authors: Romuald A. Janik, Maciej A. Nowak, Marek M. Rams, Ismail Zahed

arXiv ID: 2502.12901 | Date: 2025-02-18

Abstract: We analyze the correlation between the energy, momentum and spatial entanglement produced by two luminal jets in the massive Schwinger model. Using tensor network methods, we show that for m/g > 1/π, in the vicinity of the strong to weak coupling transition, a nearly perfect and chargeless effective fluid behavior appears around the mid-rapidity region with a universal energy-pressure relationship. The evolution of energy and pressure is strongly correlated with the rise of the spatial entanglement entropy, indicating a key role of quantum dynamics. Some of these observations may be used to analyze high multiplicity jet fragmentation events, energy-energy and energy-charge correlators at current collider energies.

Relaxation dynamics of a quantum spin coupled to a topological edge state

Authors: Qiyu Liu, Christoph Karrasch, Dante Marvin Kennes, Roman Rausch

arXiv ID: 2502.12715 | Date: 2025-02-18

Abstract: A classical impurity spin coupled to the spinful Su-Schrieffer-Heeger (SSH) chain is known to exhibit complex switching dynamics with incomplete spin relaxation. Here, we study the corrections that result from a full quantum treatment of the impurity spin. We find that in the topologically trivial case, the quantum spin behaves similarly to the classical one due to the absence of the Kondo effect for the trivial insulator. In the topological case, the quantum spin is significantly less likely to relax: It can be stuck at a pre-relaxation plateau with a sizable deviation from the expected relaxed value, and there is a large parameter regime where it does not relax at all but features an anomalously large Larmor frequency. Furthermore, we find an additional quantum effect where the pre-relaxation plateau can be hyperpolarized, i.e., the spin is stuck at a polarization value larger than the ground-state expectation value. This is possible due to the (incomplete) Kondo screening of the quantum spin, which is absent in the classical case. Our results are obtained via the ground state density matrix renormalization group (DMRG) algorithm and the time-dependent variational principle (TDVP), where the charge-SU(2) symmetry of the problem was exploited. Furthermore, we introduce and benchmark a method to predict the dynamics from the given numerical data based on the sparse identification of nonlinear dynamics (SINDy). This allows us to prolong the simulation timescale by a factor of 2.5, up to a maximal time of 10310^3 inverse hoppings.

Stability of Floquet sidebands and quantum coherence in 1D strongly interacting spinless fermions

Authors: Karun Gadge, Salvatore R. Manmana

arXiv ID: 2502.12643 | Date: 2025-02-18

Abstract: For strongly correlated quantum systems, fundamental questions about the formation and stability of Floquet-Bloch sidebands (FBs) upon periodic driving remain unresolved. Here, we investigate the impact of electron-electron interactions and perturbations in the coherence of the driving on the lifetime of FBs by directly computing time-dependent single-particle spectral functions using exact diagonalization (ED) and matrix product states (MPS). We study interacting metallic and correlated insulating phases in a chain of correlated spinless fermions. At high-frequency driving we obtain clearly separated, long-lived FBs of the full many-body excitation continuum. However, if there is significant overlap of the features, which is more probable in the low-frequency regime, the interactions lead to strong heating, which results in a significant loss of quantum coherence and of the FBs. Similar suppression of FBs is obtained in the presence of noise. The emerging picture is further elucidated by the behavior of real-space single-particle propagators, of the energy gain, and of the momentum distribution function, which is related to a quantum Fisher information that is directly accessible by spectroscopic measurements.

Matrix Product States as Observations of Entangled Hidden Markov Models

Authors: Abdessatar Souissi

arXiv ID: 2502.12641 | Date: 2025-02-18

Abstract: This paper reveals the intrinsic structure of Matrix Product States (MPS) by establishing their deep connection to entangled hidden Markov models (EHMMs). It is demonstrated that a significant class of MPS can be derived as the outcomes of EHMMs, showcasing their underlying quantum correlations. Additionally, a lower bound is derived for the relative entropy between the EHMM-observation process and the corresponding MPS, providing a quantitative measure of their informational divergence. Conversely, it is shown that every MPS is naturally associated with an EHMM, further highlighting the interplay between these frameworks. These results are supported by illustrative examples from quantum information, emphasizing their importance in understanding entanglement, quantum correlations, and tensor network representations.

Scalable Back-Propagation-Free Training of Optical Physics-Informed Neural Networks

Authors: Yequan Zhao, Xinling Yu, Xian Xiao, Zhixiong Chen, Ziyue Liu, Geza Kurczveil, Raymond G. Beausoleil, Sijia Liu, Zheng Zhang

arXiv ID: 2502.12384 | Date: 2025-02-17

Abstract: Physics-informed neural networks (PINNs) have shown promise in solving partial differential equations (PDEs), with growing interest in their energy-efficient, real-time training on edge devices. Photonic computing offers a potential solution to achieve this goal because of its ultra-high operation speed. However, the lack of photonic memory and the large device sizes prevent training real-size PINNs on photonic chips. This paper proposes a completely back-propagation-free (BP-free) and highly salable framework for training real-size PINNs on silicon photonic platforms. Our approach involves three key innovations: (1) a sparse-grid Stein derivative estimator to avoid the BP in the loss evaluation of a PINN, (2) a dimension-reduced zeroth-order optimization via tensor-train decomposition to achieve better scalability and convergence in BP-free training, and (3) a scalable on-chip photonic PINN training accelerator design using photonic tensor cores. We validate our numerical methods on both low- and high-dimensional PDE benchmarks. Through circuit simulation based on real device parameters, we further demonstrate the significant performance benefit (e.g., real-time training, huge chip area reduction) of our photonic accelerator.

Observable and computable entanglement in time

Authors: Alexey Milekhin, Zofia Adamska, John Preskill

arXiv ID: 2502.12240 | Date: 2025-02-17

Abstract: We propose a novel family of entanglement measures for time-separated subsystems. Our definitions are applicable to any quantum system, continuous or discrete. To illustrate their utility, we derive upper and lower bounds on time-separated correlation functions, akin to the bound on spatially separated correlators in terms of the mutual information. In certain cases our bounds are tight. For relativistic quantum field theories our definition agrees with the analytic continuation from spacelike to timelike separated regions. We provide relevant measurement protocols and execute them on the IBM quantum device ibm_sherbrooke for a simple qubit system. Also we perform explicit computations for an Ising spin chain, free fermions, (1+1)-dimensional conformal field theories and holographic theories. Finally we explain how the proposed entanglement in time provides a microscopic definition for the recently introduced timelike pseudoentropy.

Canted magnetism and Z2\mathbb{Z}_2 fractionalization in metallic states of the Lieb lattice Hubbard model near quarter filling

Authors: Alexander Nikolaenko, Pietro M. Bonetti, Anant Kale, Martin Lebrat, Markus Greiner, Subir Sachdev

arXiv ID: 2502.12235 | Date: 2025-02-17

Abstract: A recent experiment has examined ultracold, fermionic, spin-1/2 6^6Li atoms in the Lieb lattice at different Hubbard repulsion UU and filling fractions νν (Lebrat et al. arXiv:2404.17555). At ν=1/2ν=1/2 and small UU, they observe an enhanced compressibility on the px,yp_{x,y} sites, pointing to a flat band near the Fermi energy. At ν=1/2ν=1/2 and large UU they observe an insulating ferrimagnet. Both small and large UU observations at ν=1/2ν=1/2 are consistent with theoretical expectations. Surprisingly, near ν=1/4ν=1/4 and large UU, they again observe a large px,yp_{x,y} compressibility, pointing to a flat px,yp_{x,y} band of fermions across the Fermi energy. Our Hartree-Fock computations near ν=1/4ν=1/4 find states with canted magnetism (and related spiral states) at large UU, which possess nearly flat px,yp_{x,y} bands near the Fermi level. We employ parton theories to describe quantum fluctuations of the magnetic order found in Hartree-Fock. We find a metallic state with Z2\mathbb{Z}_2 fractionalization possessing gapless, fermionic, spinless `chargons' carrying Z2\mathbb{Z}_2 gauge charges which have a nearly flat px,yp_{x,y} band near their Fermi level: this fractionalized metal is also consistent with observations. Our DMRG study does not indicate the presence of magnetic order, and so supports a fractionalized ground state. Given the conventional ferrimagnetic insulator at ν=1/2ν=1/2, the Z2\mathbb{Z}_2 fractionalized metal at ν=1/4ν=1/4 represents a remarkable realization of doping-induced fractionalization.

Alternating and Gaussian fermionic Isometric Tensor Network States

Authors: Yantao Wu, Zhehao Dai, Sajant Anand, Sheng-Hsuan Lin, Qi Yang, Lei Wang, Frank Pollmann, Michael P. Zaletel

arXiv ID: 2502.10695 | Date: 2025-02-15

Abstract: Isometric tensor networks in two dimensions enable efficient and accurate study of quantum many-body states, yet the effect of the isometric restriction on the represented quantum states is not fully understood. We address this question in two main contributions. First, we introduce an improved variant of isometric network states (isoTNS) in two dimensions, where the isometric arrows on the columns of the network alternate between pointing upward and downward, hence the name alternating isometric tensor network states. Second, we introduce a numerical tool -- isometric Gaussian fermionic TNS (isoGfTNS) -- that incorporates isometric constraints into the framework of Gaussian fermionic tensor network states. We demonstrate in numerous ways that alternating isoTNS represent many-body ground states of two-dimensional quantum systems significantly better than the original isoTNS. First, we show that the entanglement in an isoTNS is mediated along the isometric arrows and that alternating isoTNS mediate entanglement more efficiently than conventional isoTNS. Second, alternating isoTNS correspond to a deeper, thus more representative, sequential circuit construction of depth O(LxLy)O(L_x \cdot L_y) compared to the original isoTNS of depth O(Lx+Ly)O(L_x + L_y). Third, using the Gaussian framework and gradient-based energy minimization, we provide numerical evidences of better bond-dimension scaling and variational energy of alternating isoGfTNS for ground states of various free fermionic models, including the Fermi surface, the band insulator, and the px+ipyp_x + ip_y mean-field superconductor. Finally, we find improved performance of alternating isoTNS as compared to the original isoTNS for the ground state energy of the (interacting) transverse field Ising model.

Variationally optimizing infinite projected entangled-pair states at large bond dimensions: A split corner transfer matrix renormalization group approach

Authors: Jan Naumann, Erik Lennart Weerda, Jens Eisert, Matteo Rizzi, Philipp Schmoll

arXiv ID: 2502.10298 | Date: 2025-02-14

Abstract: Projected entangled-pair states (PEPS) have become a powerful tool for studying quantum many-body systems in the condensed matter and quantum materials context, particularly with advances in variational energy optimization methods. A key challenge within this framework is the computational cost associated with the contraction of the two-dimensional lattice, crucial for calculating state vector norms and expectation values. The conventional approach, using the corner transfer matrix renormalization group (CTMRG), involves combining two tensor network layers, resulting in significant time and memory demands. In this work, we introduce an alternative "split-CTMRG" algorithm, which maintains separate PEPS layers and leverages new environment tensors, reducing computational complexity while preserving accuracy. Benchmarks on quantum lattice models demonstrate substantial speedups for variational energy optimization, rendering this method valuable for large-scale PEPS simulations.

Deep Tree Tensor Networks for Image Recognition

Authors: Chang Nie, Junfang Chen, Yajie Chen

arXiv ID: 2502.09928 | Date: 2025-02-14

Abstract: Originating in quantum physics, tensor networks (TNs) have been widely adopted as exponential machines and parameter decomposers for recognition tasks. Typical TN models, such as Matrix Product States (MPS), have not yet achieved successful application in natural image processing. When employed, they primarily serve to compress parameters within off-the-shelf networks, thus losing their distinctive capability to enhance exponential-order feature interactions. This paper introduces a novel architecture named \textit{\textbf{D}eep \textbf{T}ree \textbf{T}ensor \textbf{N}etwork} (DTTN), which captures 2L2^L-order multiplicative interactions across features through multilinear operations, while essentially unfolding into a \emph{tree}-like TN topology with the parameter-sharing property. DTTN is stacked with multiple antisymmetric interacting modules (AIMs), and this design facilitates efficient implementation. Moreover, we theoretically reveal the equivalency among quantum-inspired TN models and polynomial and multilinear networks under certain conditions, and we believe that DTTN can inspire more interpretable studies in this field. We evaluate the proposed model against a series of benchmarks and achieve excellent performance compared to its peers and cutting-edge architectures. Our code will soon be publicly available.

Floquet Engineering and Harnessing Giant Atoms in Frequency-Comb Emission and Bichromatic Correlations in Waveguide QED

Authors: Qing-Yang Qiu, Li-Li Zheng, Ying Wu, Xin-You Lu

arXiv ID: 2502.09901 | Date: 2025-02-14

Abstract: The capability to design spectrally controlled photon emission is not only fundamentally interesting for understanding frequency-encoded light-matter interactions, but also is essential for realizing the preparation and manipulation of quantum states. Here we consider a dynamically modulated qubit array, and realize frequency-controlled single-photon emission focusing on the generation of a frequency comb constituted solely of even-parity or anti-Stokes sidebands. Our system also offers parity-dependent bunching and antibunching in frequency-filtered quantum correlations. In particular, the waveguide quantum electrodynamics (QED) setup is extended to include chiral and non-local coupling architectures, thereby enhancing its versatility in Floquet engineering. Our proposal also supports the predictable generation of high-dimensional entangled quantum states, where the corresponding effective Hilbert space dimension is well controlled by energy modulation. Moreover, the utilisation of sophisticated numerical tools, such as the matrix product states (MPSs) and the discretization approach, enables the efficient simulation of multi-photon dynamics, in which the non-Markovian Floquet steady states emerge. This work fundamentally broadens the fields of collective emission, and has wide applications in implementing frequency-encoded quantum information processing and many-body quantum simulation.

Non-stabilizerness of Neural Quantum States

Authors: Alessandro Sinibaldi, Antonio Francesco Mello, Mario Collura, Giuseppe Carleo

arXiv ID: 2502.09725 | Date: 2025-02-13

Abstract: We introduce a methodology to estimate non-stabilizerness or "magic", a key resource for quantum complexity, with Neural Quantum States (NQS). Our framework relies on two schemes based on Monte Carlo sampling to quantify non-stabilizerness via Stabilizer Rényi Entropy (SRE) in arbitrary variational wave functions. When combined with NQS, this approach is effective for systems with strong correlations and in dimensions larger than one, unlike Tensor Network methods. Firstly, we study the magic content in an ensemble of random NQS, demonstrating that neural network parametrizations of the wave function capture finite non-stabilizerness besides large entanglement. Secondly, we investigate the non-stabilizerness in the ground state of the J1J_1-J2J_2 Heisenberg model. In 1D, we find that the SRE vanishes at the Majumdar-Ghosh point J2=J1/2J_2 = J_1/2, consistent with a stabilizer ground state. In 2D, a dip in the SRE is observed near maximum frustration around J2/J10.6J_2/J_1 \approx 0.6, suggesting a Valence Bond Solid between the two antiferromagnetic phases.

Fast Tensor Completion via Approximate Richardson Iteration

Authors: Mehrdad Ghadiri, Matthew Fahrbach, Yunbum Kook, Ali Jadbabaie

arXiv ID: 2502.09534 | Date: 2025-02-13

Abstract: We study tensor completion (TC) through the lens of low-rank tensor decomposition (TD). Many TD algorithms use fast alternating minimization methods to solve highly structured linear regression problems at each step (e.g., for CP, Tucker, and tensor-train decompositions). However, such algebraic structure is often lost in TC regression problems, making direct extensions unclear. This work proposes a novel lifting method for approximately solving TC regression problems using structured TD regression algorithms as blackbox subroutines, enabling sublinear-time methods. We analyze the convergence rate of our approximate Richardson iteration-based algorithm, and our empirical study shows that it can be 100x faster than direct methods for CP completion on real-world tensors.

Quantum Speed Limit and Quantum Thermodynamic Uncertainty Relation under Feedback Control

Authors: Hayato Yunoki, Yoshihiko Hasegawa

arXiv ID: 2502.09081 | Date: 2025-02-13

Abstract: Fundamental trade-off relations, such as quantum speed limit and quantum thermodynamic uncertainty relation, describe the performance limits of quantum systems by imposing that improvements in speed or precision necessitate a substantial thermodynamic cost. Quantum feedback control, which is a pivotal technique for manipulating quantum dynamics based on measurement outcomes, is widely employed to enhance system performance. Nevertheless, its impact on these fundamental bounds remains an open question. This work elucidates this influence by establishing a theoretical framework for quantum speed limit and quantum thermodynamic uncertainty relation under a paradigmatic Markovian feedback protocol. We derive general inequalities incorporating the effects of feedback control on speed and precision. Through numerical simulations on a simple two-level system and quantum error correction, a key application of quantum feedback control, we validate our derived bounds and demonstrate that feedback control can indeed improve both speed and precision beyond those achievable limits in uncontrolled systems. Next, to elucidate the mechanism behind these improvements and the qualitative difference from uncontrolled dynamics, we analyze the governing thermodynamic costs, which are the fundamental quantities that constrain speed and precision, within a simple model. Our analysis reveals that feedback can improve the time scaling order of these costs. This modification of the dynamical scaling is the origin of the qualitative performance gain, signifying that the feedback-induced improvements of performance are not merely quantitative but represent a fundamental shift. Consequently, our work offers a comprehensive understanding of how feedback control impacts the fundamental limits on the speed and precision of quantum systems, providing crucial insights for designing high-performance quantum technologies.

Dynamics of the Bose-Hubbard Model Induced by On-Site or Long-Range Two-Body Losses

Authors: Julien Despres, Leonardo Mazza, Marco Schirò

arXiv ID: 2502.09008 | Date: 2025-02-13

Abstract: We present a theoretical study of the dissipative dynamics of the Bose-Hubbard model induced by on-site or long-range two-body losses. We first consider the one-dimensional chain and the two-dimensional square lattice, and study the dynamics induced by the sudden switch-on of two-body losses on a weakly-interacting superfluid state. The time-dependent density is obtained in the spirit of the Bogolyubov approach by calculating theoretically the equations of motion associated to the relevant quadratic bosonic correlators. In the one-dimensional case, our results compare very well with quasi-exact numerical calculations based on the quantum jump method implemented using tensor networks. We find that the intermediate-time dynamics of the density displays an algebraic decay characterized by an interaction-dependent power-law exponent. The latter property still holds for long-range two-body loss processes but it is absent in the two-dimensional square lattice with on-site losses.

The Saga of αα-RuCl3_3: Parameters, Models, and Phase Diagrams

Authors: Marius Möller, P. A. Maksimov, Shengtao Jiang, Steven R. White, Roser Valenti, A. L. Chernyshev

arXiv ID: 2502.08698 | Date: 2025-02-12

Abstract: RuCl3_3 was likely the first ever deliberately synthesized ruthenium compound, following the discovery of the 44_{44}Ru element in 1844. For a long time it was known as an oxidation catalyst, with its physical properties being discrepant and confusing, until a decade ago when its allotropic form αα-RuCl3_3 rose to exceptional prominence. This "re-discovery" of αα-RuCl3_3 has not only reshaped the hunt for a material manifestation of the Kitaev spin liquid, but it has opened the floodgates of theoretical and experimental research in the many unusual phases and excitations that the anisotropic-exchange magnets as a class of compounds have to offer. Given its importance for the field of Kitaev materials, it is astonishing that the low-energy spin model that describes this compound and its possible proximity to the much-desired spin-liquid state is still a subject of significant debate ten years later. In the present study, we argue that the existing key phenomenological observations put strong natural constraints on the effective microscopic spin model of αα-RuCl3_3, and specifically on its spin-orbit-induced anisotropic-exchange parameters that are responsible for the non-trivial physical properties of this material. These constraints allow one to focus on the relevant region of the multi-dimensional phase diagram of the αα-RuCl3_3 model, suggest an intuitive description of it via a different parametrization of the exchange matrix, offer a unifying view on the earlier assessments of its parameters, and bring closer together several approaches to the derivation of anisotropic-exchange models. We explore extended phase diagrams relevant to the αα-RuCl3_3 parameter space using quasi-classical, Luttinger-Tisza, exact diagonalization, and density-matrix renormalization group methods, demonstrating a remarkably c... (arxiv cutoff; for the rest, see the paper)

Kitaev-Ising-J1J_1-J2J_2 model: a density matrix renormalization group study

Authors: A. V. Kapranov, R. S. Akzyanov

arXiv ID: 2502.08389 | Date: 2025-02-12

Abstract: We numerically study the Kitaev honeycomb model with the additional XX Ising interaction between the nearest and the next nearest neighbors (Kitaev-Ising-J1J_1-J2J_2 model), by using the density matrix renormalization group (DMRG) method. Such additional interaction correspond to the nearest and diagonal interactions on the square lattice. Phase diagram of the bare Kitaev model consist of low entangled commensurate magnetic phases and entagled Kitaev spin liquid. Anisotropic Ising interaction allows the entangled incommensurate magnetic phases in the phase diagram, which previously was predicted only for more complex type of interactions. We study the scaling law of the entanglement entropy and the bond dimension of the matrix product state with the size of the system. In addition, we propose an optimization algorithm to prevent DMRG from getting stuck in the low-entangled phases.

Probing the many-body localized spin-glass phase through quench dynamics

Authors: Pietro Brighi, Marko Ljubotina, Maksym Serbyn

arXiv ID: 2502.08192 | Date: 2025-02-12

Abstract: Eigenstates of quantum many-body systems are often used to define phases of matter in and out of equilibrium; however, experimentally accessing highly excited eigenstates is a challenging task, calling for alternative strategies to dynamically probe nonequilibrium phases. In this work, we characterize the dynamical properties of a disordered spin chain, focusing on the spin-glass regime. Using tensor-network simulations, we observe oscillatory behavior of local expectation values and bipartite entanglement entropy. We explain these oscillations deep in the many-body localized spin glass regime via a simple theoretical model. From perturbation theory, we predict the timescales up to which our analytical description is valid and confirm it with numerical simulations. Finally, we study the correlation length dynamics, which, after a long-time plateau, resumes growing in line with renormalization group (RG) expectations. Our work suggests that RG predictions can be quantitatively tested against numerical simulations and experiments, potentially enabling microscopic descriptions of dynamical phases in large systems.

Lattice Defects in Rydberg Atom Arrays

Authors: Hanteng Wang, Chengshu Li, Xingyu Li, Yingfei Gu, Shang Liu

arXiv ID: 2502.07886 | Date: 2025-02-11

Abstract: Rydberg atom arrays have become a key platform for studying quantum many-body systems. In these setups, defects arise naturally due to various imperfections and can significantly modify the theoretical predictions compared to an ideal model. Here, we investigate the impact of geometric defects in the simplest situation -- a one-dimensional Rydberg atom array, both at and away from its emergent Ising criticality. In the presence of defects, we demonstrate that relevant physical quantities can be extracted from one-point correlation functions. At the critical point, we show that different types of kinks yield distinct outcomes corresponding to their respective spatial-internal symmetries: site-centered kinks can effectively break the array at the kink position regardless of the kink angle, while bond-centered kinks lead to interesting intermediate-coupling fixed points. In the latter case, due to a special renormalization group flow trajectory, the whole system can appear ordered if the system is not large enough. Additionally, away from criticality, the bond-centered kink induces a localization-delocalization transition of the domain wall, characteristic of quantum wetting. These findings highlight the utility of kinks as experimental probes and stress the importance of controlling defects so that experimental observations remain faithful to the pristine model.

Lagrangian Attention Tensor Networks for Velocity Gradient Statistical Modeling

Authors: Criston Hyett, Yifeng Tian, Michael Woodward, Misha Stepanov, Chris Fryer, Daniel Livescu, Michael Chertkov

arXiv ID: 2502.07078 | Date: 2025-02-10

Abstract: Direct numerical simulation of turbulence at realistic Reynolds numbers is still beyond current computational capability, necessitating models that reduce the number of resolved spatial scales. Motivated by phenomenology and recent data-driven works based on universality of the smallest scales in fully developed turbulence, the statistical dynamics of the velocity gradient tensor (VGT) at the Kolmogorov scale become of critical importance in advancing turbulence models. Physics-informed machine learning has found considerable success in exploiting large datasets taken from direct numerical simulation of Navier-Stokes to improve models for the evolution of the VGT. In this work, we follow the long line of blending physical insight with data analysis to simultaneously advance both the modeling and understanding of the phenomenology of the VGT. Using the intimate connection between VGT evolution and fluid deformation, we develop the Lagrangian attention tensor network approach that significantly improves over current physics-informed machine learning methods. We demonstrate state-of-the-art performance in both a-priori and a-posteriori metrics, before interpreting the trained attention mechanisms to discover a surprising connection between the history of the strain-rate-tensor and the pressure Hessian.

Fully optimised variational simulation of a dynamical quantum phase transition on a trapped-ion quantum computer

Authors: Lesley Gover, Vinul Wimalaweera, Fariha Azad, Matthew DeCross, Michael Foss-Feig, Andrew G. Green

arXiv ID: 2502.06961 | Date: 2025-02-10

Abstract: We time-evolve a translationally invariant quantum state on the Quantinuum H1-1 trapped-ion quantum processor, studying the dynamical quantum phase transition of the transverse field Ising model. This physics requires a delicate cancellation of phases in the many-body wavefunction and presents a tough challenge for current quantum devices. We follow the dynamics using a quantum circuit matrix product state ansatz, optimised for the time-evolution using a fidelity cost function. Sampling costs are mitigated by using the measured values of this circuit as stochastic corrections to a simple classical extrapolation of the ansatz parameters. Our results demonstrate the feasibility of variational quantum time-evolution and reveal a hitherto hidden simplicity of the evolution of the transverse-field Ising model through the dynamical quantum phase transition.

Computing Quantum Resources using Tensor Cross Interpolation

Authors: Sven Benjamin Kožić, Gianpaolo Torre

arXiv ID: 2502.06956 | Date: 2025-02-10

Abstract: Quantum information quantifiers are indispensable tools for analyzing strongly correlated systems. Consequently, developing efficient and robust numerical methods for their computation is crucial. We propose a general procedure based on the family of Tensor Cross Interpolation (TCI) algorithms to address this challenge in a fully general framework, independent of the system or the quantifier under consideration. To substantiate our approach, we compute the non-stabilizerness Rényi entropy (SRE) and Relative Entropy of Coherence (REC) considering the 1D and 2D ferromagnetic Ising models with minimal modifications to the numerical procedure. This method not only demonstrates its versatility, but also provides a generic framework for exploring other quantum information quantifiers in complex systems.

Exact NESS of XXZ circuits boundary driven with arbitrary resets or fields

Authors: Vladislav Popkov, Tomaž Prosen

arXiv ID: 2502.06731 | Date: 2025-02-10

Abstract: We propose spatially inhomogeneous matrix product ansatz for an exact many-body density operator of a boundary driven XXZ quantum circuit. The ansatz has formally infinite bond-dimension and is fundamentally different from previous constructions. The circuit is driven by a pair of reset quantum channels applied on the boundary qubits, which polarize the qubits to arbitrary pure target states. Moreover, one of the reset channels can be replaced by an arbitrary local unitary gate, thus representing a hybrid case with coherent/incoherent driving. Analyzing the ansatz we obtain a family of relatively robust separable nonequilibrium steady states (NESS), which can be viewed as a circuit extension of spin-helix states, and are particularly suited for experimental investigations.

Floquet-Engineered Hybrid Topological Orders with Majorana Edge Modes in Number-Conserving Fermionic Quantum Simulators

Authors: Zhi Lin, Qi Song, Sheng Yue, Ming Yang, Jie Lou, Yan Chen

arXiv ID: 2502.06569 | Date: 2025-02-10

Abstract: We develop an experimental protocol based on Floquet-engineered ultracold fermions in optical lattices, enabling the emulation of pair-hopping and competing singlet/triplet pairing interactions. Through large-scale density matrix renormalization group (DMRG) simulations, we uncover three emergent topological phases: (i) A Majorana-enabled spin-density-wave (MS) phase featuring exponentially localized edge charges, non-local fermionic edge correlations, and doubly degenerate entanglement spectra; (ii) A z-axis polarized triplet superconducting (TS) phase exhibiting fractionalized edge spins (S=1/4 per edge), two-fold ground state degeneracy and a bulk single-particle gap; (iii) A hybrid x-directional triplet superconducting (XTS) phase that uniquely combines fractional spin textures and Majorana-type edge correlations, defining a new universality class of hybrid orders in number-conserving systems. These findings establish a universal framework for engineering non-Abelian topological matter, crucially bypassing the need for external pairing fields while maintaining experimental feasibility with current cold-atom techniques.

Phase structure analysis of CP(1) model with θθ term by tensor renormalization group

Authors: Hayato Aizawa, Shinji Takeda, Yusuke Yoshimura

arXiv ID: 2502.06135 | Date: 2025-02-10

Abstract: We analyze the phase structure of 2d lattice CP(1) model with θθ term by using the bond-weighted tensor renormalization group method. We propose a new tensor network representation for the model using the quadrature scheme and confirm that its accuracy is better than that of the conventional character-like expansion. As a probe to study the phase structure, we adopt the central charge and the scaling dimensions. The numerical results indicate an existence of critical point at θ=πθ=π, which is consistent with the Haldane's conjecture.

Explicit Solution Equation for Every Combinatorial Problem via Tensor Networks: MeLoCoToN

Authors: Alejandro Mata Ali

arXiv ID: 2502.05981 | Date: 2025-02-09

Abstract: In this paper we show that every combinatorial problem has an exact explicit equation that returns its solution. We present a method to obtain an equation that solves exactly any combinatorial problem, both inversion, constraint satisfaction and optimization, by obtaining its equivalent tensor network. This formulation only requires a basic knowledge of classical logical operators, at a first year level of any computer science degree. These equations are not necessarily computable in a reasonable time, nor do they allow to surpass the state of the art in computational complexity, but they allow to have a new perspective for the mathematical analysis of these problems. These equations computation can be approximated by different methods such as Matrix Product State compression. We also present the equations for numerous combinatorial problems. This work proves that, if there is a physical system capable of contracting in polynomial time the tensor networks presented, every NP-Hard problem can be solved in polynomial time.

Qubit Regularization of Quantum Field Theories

Authors: Shailesh Chandrasekharan

arXiv ID: 2502.05716 | Date: 2025-02-08

Abstract: To study quantum field theories on a quantum computer, we must begin with Hamiltonians defined on a finite-dimensional Hilbert space and then take appropriate limits. This approach can be seen as a new type of regularization for quantum field theories, which we refer to as qubit regularization. A related finite-dimensional regularization, known as the D-theory approach, was proposed long ago as a general framework for all quantum field theories. In this framework, the dimensionality of the local Hilbert space at each spatial point can increase as needed through an additional flavor index. To reproduce asymptotically free QFTs, most studies assume that qubit-regularized theories require extending the local Hilbert space to infinity. However, contrary to this common belief, recent discoveries in (1+1) dimensions have revealed two examples where asymptotic freedom appears to emerge within a strictly finite-dimensional local Hilbert space through a novel renormalization group (RG) flow. These findings motivate further investigation into whether asymptotically free gauge theories could also emerge within a strictly finite-dimensional local Hilbert space. To support these explorations, we propose an orthonormal basis called the monomer-dimer-tensor-network (MDTN) basis and use it to construct new types of qubit-regularized lattice gauge theories.

Anomalous suppression of large-scale density fluctuations in classical and quantum spin liquids

Authors: Duyu Chen, Rhine Samajdar, Yang Jiao, Salvatore Torquato

arXiv ID: 2502.05313 | Date: 2025-02-07

Abstract: Classical spin liquids (CSLs) are intriguing states of matter that do not exhibit long-range magnetic order and are characterized by an extensive ground-state degeneracy. Adding quantum fluctuations, which induce dynamics between these different classical ground states, can give rise to quantum spin liquids (QSLs). QSLs are highly entangled quantum phases of matter characterized by fascinating emergent properties, such as fractionalized excitations and topological order. One such exotic quantum liquid is the Z2\mathbb{Z}_2 QSL, which can be regarded as a resonating valence bond (RVB) state formed from superpositions of dimer coverings of an underlying lattice. In this work, we unveil a \textit{hidden} large-scale structural property of archetypal CSLs and QSLs known as hyperuniformity, i.e., normalized infinite-wavelength density fluctuations are completely suppressed in these systems. In particular, we first demonstrate that classical ensembles of close-packed dimers and their corresponding quantum RVB states are perfectly hyperuniform in general. Subsequently, we focus on a ruby-lattice spin liquid that was recently realized in a Rydberg-atom quantum simulator, and show that the QSL remains effectively hyperuniform even in the presence of a finite density of spinon and vison excitations, as long as the dimer constraint is still largely preserved. Moreover, we demonstrate that metrics based on the framework of hyperuniformity can be used to distinguish the QSL from other proximate quantum phases. These metrics can help identify potential QSL candidates, which can then be further analyzed using more advanced, computationally-intensive quantum numerics to confirm their status as true QSLs.

Gaussian Models to Non-Gaussian Realms of Quantum Photonic Simulators

Authors: Dennis Delali Kwesi Wayo, Rodrigo Alves Dias, Masoud Darvish Ganji, Camila Martins Saporetti, Leonardo Goliatt

arXiv ID: 2502.05245 | Date: 2025-02-07

Abstract: Quantum photonic simulators have emerged as indispensable tools for modeling and optimizing quantum photonic circuits, bridging the gap between theoretical models and experimental implementations. This review explores the landscape of photonic quantum simulation, focusing on the transition from Gaussian to non-Gaussian models and the computational challenges associated with simulating large-scale photonic systems. Gaussian states and operations, which enable efficient simulations through covariance matrices and phase-space representations, serve as the foundation for photonic quantum computing. However, non-Gaussian states crucial for universal quantum computation introduce significant computational complexity, requiring advanced numerical techniques such as tensor networks and high-performance GPU acceleration. We evaluate the leading photonic quantum simulators, including Strawberry Fields, Piquasso, QuTiP SimulaQron, Perceval, and QuantumOPtics.jl analyzing their capabilities in handling continuous-variable (CV) and discrete-variable (DV) quantum systems. Special attention is given to hardware-accelerated methods, including GPU-based tensor network approaches, machine learning integration, and hybrid quantum-classical workflows. Furthermore, we investigate noise modeling techniques, such as photon loss and dark counts, and their impact on simulation accuracy. As photonic quantum computing moves toward practical implementations, advancements in high-performance computing (HPC) architectures, such as tensor processing units (TPUs) and system-on-a-chip (SoC) solutions, are accelerating the field. This review highlights emerging trends, challenges, and future directions for developing scalable and efficient photonic quantum simulators.

Generative-enhanced optimization for knapsack problems: an industry-relevant study

Authors: Yelyzaveta Vodovozova, Abhishek Awasthi, Caitlin Jones, Joseph Doetsch, Karen Wintersperger, Florian Krellner, Carlos A. Riofrío

arXiv ID: 2502.04928 | Date: 2025-02-07

Abstract: Optimization is a crucial task in various industries such as logistics, aviation, manufacturing, chemical, pharmaceutical, and insurance, where finding the best solution to a problem can result in significant cost savings and increased efficiency. Tensor networks (TNs) have gained prominence in recent years in modeling classical systems with quantum-inspired approaches. More recently, TN generative-enhanced optimization (TN-GEO) has been proposed as a strategy which uses generative modeling to efficiently sample valid solutions with respect to certain constraints of optimization problems. Moreover, it has been shown that symmetric TNs (STNs) can encode certain constraints of optimization problems, thus aiding in their solution process. In this work, we investigate the applicability of TN- and STN-GEO to an industry relevant problem class, a multi-knapsack problem, in which each object must be assigned to an available knapsack. We detail a prescription for practitioners to use the TN-and STN-GEO methodology and study its scaling behavior and dependence on its hyper-parameters. We benchmark 60 different problem instances and find that TN-GEO and STN-GEO produce results of similar quality to simulated annealing.

High-dimensional stochastic finite volumes using the tensor train format

Authors: Juliette Dubois, Michael Herty, Siegfried Müller

arXiv ID: 2502.04868 | Date: 2025-02-07

Abstract: A method for the uncertainty quantification of nonlinear hyperbolic equations with many uncertain parameters is presented. The method combines the stochastic finite volume method and tensor trains in a novel way: the physical space and time dimensions are kept as full tensors, while all stochastic dimensions are compressed together into a tensor train. The resulting hybrid format has one tensor train for each spatial cell and each time step. The MUSCL scheme is adapted to this hybrid format and the feasibility of the approach using several classical test cases is shown. For the Burgers' equation a convergence study and a comparison with the full tensor train format are done with three stochastic parameters. The equation is then solved for an increasing number of stochastic dimensions. The Euler equations are then considered. A parameter study and a comparison with the full tensor train format are performed with the Sod problem. For a complex application we consider the Shu-Osher problem. The presented method opens new avenues for combining uncertainty quantification with well-known numerical schemes for conservation laws.

Crossover from Wannier-Stark localization to charge density waves for interacting spinless fermions in one dimension

Authors: Nair Aucar Boidi, Amnon Aharony, Ora Entin-Wohlman, Karen Hallberg, Cesar Proetto

arXiv ID: 2502.04866 | Date: 2025-02-07

Abstract: We study spinless fermions on a finite chain with nearest-neighbor repulsion and in the presence of a Wannier-Stark linearly-varying electric field potential. In the absence of the interaction, the eigenstates are localized for the system's sizes larger than the localization length. We present several analytical expressions for the localization length, which is proportional to the inverse of the electric field. Using the density matrix renormalization group numerical technique, we observe that the ground state exhibits a decrease of the occupation on the chain sites from the `bulk', with occupation 1, to the vacuum, with occupation 0. The width of this intermediate `edge' region is also inversely proportional to the electric field, increasing linearly with the strength of the nearest-neighbor repulsion. For strong interactions, the occupations in the intermediate region exhibit a charge density wave. We also present the local density of states for sites in the `edge' region. For the non-interacting case, the spectrum shows an increasing energy-localized structure as the field is increased, which is a consequence of the uniform energy distribution of the localized states (Wannier-Stark ladder). This structure survives for small interactions, and it smears out in the strongly interacting limit. Experimental variations of the slope of the potential (the electric field) on cold atom chains may test these predictions.

Tensor-Programmable Quantum Circuits for Solving Differential Equations

Authors: Pia Siegl, Greta Sophie Reese, Tomohiro Hashizume, Nis-Luca van Hülst, Dieter Jaksch

arXiv ID: 2502.04425 | Date: 2025-02-06

Abstract: We present a quantum solver for partial differential equations based on a flexible matrix product operator representation. Utilizing mid-circuit measurements and a state-dependent norm correction, this scheme overcomes the restriction of unitary operators. Hence, it allows for the direct implementation of a broad class of differential equations governing the dynamics of classical and quantum systems. The capabilities of the framework are demonstrated for linear and non-linear partial differential equations using the example of the linearized Euler equations with absorbing boundaries and the nonlinear Burgers' equation. For a turbulence data set, we demonstrate potential advantages of the quantum tensor scheme over its classical counterparts.

Tensor Decomposition Meets Knowledge Compilation: A Study Comparing Tensor Trains with OBDDs

Authors: Ryoma Onaka, Kengo Nakamura, Masaaki Nishino, Norihito Yasuda

arXiv ID: 2502.03702 | Date: 2025-02-06

Abstract: A knowledge compilation map analyzes tractable operations in Boolean function representations and compares their succinctness. This enables the selection of appropriate representations for different applications. In the knowledge compilation map, all representation classes are subsets of the negation normal form (NNF). However, Boolean functions may be better expressed by a representation that is different from that of the NNF subsets. In this study, we treat tensor trains as Boolean function representations and analyze their succinctness and tractability. Our study is the first to evaluate the expressiveness of a tensor decomposition method using criteria from knowledge compilation literature. Our main results demonstrate that tensor trains are more succinct than ordered binary decision diagrams (OBDDs) and support the same polytime operations as OBDDs. Our study broadens their application by providing a theoretical link between tensor decomposition and existing NNF subsets.

Page Curve and Entanglement Dynamics in an Interacting Fermionic Chain

Authors: Rishabh Jha, Salvatore R. Manmana, Stefan Kehrein

arXiv ID: 2502.03563 | Date: 2025-02-05

Abstract: Generic non-equilibrium many-body systems display a linear growth of bipartite entanglement entropy in time, followed by a volume law saturation. In stark contrast, the Page curve dynamics of black hole physics shows that the entropy peaks at the Page time tPaget_{\text{Page}} and then decreases to zero. Here, we investigate such Page-like behavior of the von Neumann entropy in a model of strongly correlated spinless fermions in a typical system-environment setup, and characterize the properties of the Page curve dynamics in the presence of interactions using numerically exact matrix product states methods. The two phases of growth, namely the linear growth and the bending down, are shown to be separated by a non-analyticity in the min-entropy before tPaget_{\text{Page}}, which separates two different quantum phases, realized as the respective ground states of the corresponding entanglement (or equivalently, modular) Hamiltonian. We confirm and generalize, by introducing interactions, the findings of \href{https://journals.aps.org/prb/abstract/10.1103/PhysRevB.109.224308}{Phys. Rev. B 109, 224308 (2024)} for a free spinless fermionic chain where the corresponding entanglement Hamiltonian undergoes a quantum phase transition at the point of non-analyticity. However, in the presence of interactions, a scaling analysis gives a non-zero critical time for the non-analyticity in the thermodynamic limit only for weak to intermediate interaction strengths, while the dynamics leading to the non-analyticity becomes \textit{instantaneous} for interactions large enough. We present a physical picture explaining these findings.

TensorQC: Towards Scalable Distributed Quantum Computing via Tensor Networks

Authors: Wei Tang, Margaret Martonosi

arXiv ID: 2502.03445 | Date: 2025-02-05

Abstract: A quantum processing unit (QPU) must contain a large number of high quality qubits to produce accurate results for problems at useful scales. In contrast, most scientific and industry classical computation workloads happen in parallel on distributed systems, which rely on copying data across multiple cores. Unfortunately, copying quantum data is theoretically prohibited due to the quantum non-cloning theory. Instead, quantum circuit cutting techniques cut a large quantum circuit into multiple smaller subcircuits, distribute the subcircuits on parallel QPUs and reconstruct the results with classical computing. Such techniques make distributed hybrid quantum computing (DHQC) a possibility but also introduce an exponential classical co-processing cost in the number of cuts and easily become intractable. This paper presents TensorQC, which leverages classical tensor networks to bring an exponential runtime advantage over state-of-the-art parallelization post-processing techniques. As a result, this paper demonstrates running benchmarks that are otherwise intractable for a standalone QPU and prior circuit cutting techniques. Specifically, this paper runs six realistic benchmarks using QPUs available nowadays and a single GPU, and reduces the QPU size and quality requirements by more than 10×10\times over purely quantum platforms.

Observation of slow relaxation due to Hilbert space fragmentation in strongly interacting Bose-Hubbard chains

Authors: Kantaro Honda, Yosuke Takasu, Shimpei Goto, Hironori Kazuta, Masaya Kunimi, Ippei Danshita, Yoshiro Takahashi

arXiv ID: 2502.02959 | Date: 2025-02-05

Abstract: While isolated quantum systems generally thermalize after long-time evolution, there are several exceptions defying thermalization. A notable mechanism of such nonergodicity is the Hilbert space fragmentation (HSF), where the Hamiltonian matrix splits into an exponentially large number of sectors due to the presence of nontrivial conserved quantities. Using ultracold gases, here we experimentally investigate the one-dimensional Bose-Hubbard system with neither disorder nor tilt potential, which has been predicted to exhibit HSF caused by a strong interatomic interaction. Specifically, we analyze far-from-equilibrium dynamics starting from a charge-density wave of doublons (atoms in doubly occupied sites) in a singlon and doublon-resolved manner to reveal a slowing-down of the relaxation in a strongly interacting regime. We find that the numbers of singlons and doublons are conserved during the dynamics, indicating HSF as a mechanism of the observed slow relaxation. Our results provide an experimental confirmation of the conserved quantities responsible for HSF.

Quantum State Preparation via Nested Entanglement

Authors: Geoffrey L. Warner

arXiv ID: 2502.02784 | Date: 2025-02-05

Abstract: We develop a representation of an n-qubit register that parameterizes its statevector as a series of nested entanglements. We show that the recursive substructure of this representation provides a natural framework for automating the construction of quantum circuits for state preparation. It also allows for a straightforward treatment of pure state separability. We discuss a novel derivation of uniformly controlled rotations and the quantum Fourier transform within this representation, and consider the effects of single-qubit basis changes on its overall structure. We end with a discussion of the apparent connection between the compressibility of the state description in this representation, and the circuit complexity required to prepare it.

Tensor Network Structure Search with Program Synthesis

Authors: Zheng Guo, Aditya Deshpande, Brian Kiedrowski, Xinyu Wang, Alex Gorodetsky

arXiv ID: 2502.02711 | Date: 2025-02-04

Abstract: Tensor networks provide a powerful framework for compressing multi-dimensional data. The optimal tensor network structure for a given data tensor depends on both data characteristics and specific optimality criteria, making tensor network structure search a difficult problem. Existing solutions typically rely on sampling and compressing numerous candidate structures; these procedures are computationally expensive and therefore limiting for practical applications. We address this challenge by viewing tensor network structure search as a program synthesis problem and introducing an efficient constraint-based assessment method that avoids costly tensor decomposition. Specifically, we establish a correspondence between transformation programs and network structures. We also design a novel operation named output-directed splits to reduce the search space without hindering expressiveness. We then propose a synthesis algorithm to identify promising network candidates through constraint solving, and avoid tensor decomposition for all but the most promising candidates. Experimental results show that our approach improves search speed by up to 10×10\times and achieves compression ratios 1.5×1.5\times to 3×3\times better than state-of-the-art. Notably, our approach scales to larger tensors that are unattainable by prior work. Furthermore, the discovered topologies generalize well to similar data, yielding compression ratios up to 2.4×2.4\times better than a generic structure while the runtime remains around 110110 seconds.

SpinGlassPEPS.jl: Tensor-network package for Ising-like optimization on quasi-two-dimensional graphs

Authors: Tomasz Śmierzchalski, Anna M. Dziubyna, Konrad Jałowiecki, Zakaria Mzaouali, Łukasz Pawela, Bartłomiej Gardas, Marek M. Rams

arXiv ID: 2502.02317 | Date: 2025-02-04

Abstract: This work introduces SpinGlassPEPS..jl, a software package implemented in Julia, designed to find low-energy configurations of generalized Potts models, including Ising and QUBO problems, utilizing heuristic tensor network contraction algorithms on quasi-2D geometries. In particular, the package employs the Projected Entangled-Pairs States to approximate the Boltzmann distribution corresponding to the model's cost function. This enables an efficient branch-and-bound search (within the probability space) that exploits the locality of the underlying problem's topology. As a result, our software enables the discovery of low-energy configurations for problems on quasi-2D graphs, particularly those relevant to modern quantum annealing devices. The modular architecture of SpinGlassPEPS..jl supports various contraction schemes and hardware acceleration.

Entanglement entropy by tensor renormalization group approach

Authors: Takahiro Hayazaki, Daisuke Kadoh, Shinji Takeda, Gota Tanaka

arXiv ID: 2502.02030 | Date: 2025-02-04

Abstract: We report on tensor renormalization group calculations of entanglement entropy in one-dimensional quantum systems. The reduced density matrix of a Gibbs state can be represented as a 1+11 + 1-dimensional tensor network, which is analogous to the tensor network representation of the partition function. The HOTRG method is used to approximate the reduced density matrix for arbitrary subsystem sizes, from which we obtain the entanglement entropy. We test our method in the quantum Ising model and obtain the entanglement entropy of the ground state by taking the size of time direction to infinity. The central charge cc is obtained as c=0.49997(8)c = 0.49997(8) for a bond dimension D=96D=96, which agrees with the theoretical value c=1/2c=1/2 within the error.

Complex entanglement entropy for complex conformal field theory

Authors: Haruki Shimizu, Kohei Kawabata

arXiv ID: 2502.02001 | Date: 2025-02-04

Abstract: Conformal field theory underlies critical ground states of quantum many-body systems. While conventional conformal field theory is associated with positive central charges, nonunitary conformal field theory with complex-valued central charges has recently been recognized as physically relevant. Here, we demonstrate that complex-valued entanglement entropy characterizes complex conformal field theory and critical phenomena of open quantum many-body systems. This is based on non-Hermitian reduced density matrices constructed from the combination of right and left ground states. Applying the density matrix renormalization group to non-Hermitian systems, we numerically calculate the complex entanglement entropy of the non-Hermitian five-state Potts model, thereby confirming the scaling behavior predicted by complex conformal field theory.

Clifford-Dressed Variational Principles for Precise Loschmidt Echoes

Authors: Antonio Francesco Mello, Alessandro Santini, Mario Collura

arXiv ID: 2502.01872 | Date: 2025-02-03

Abstract: We extend the recently introduced Clifford dressed Time-Dependent Variational Principle (TDVP) to efficiently compute many-body wavefunction amplitudes in the computational basis. This advancement enhances the study of Loschmidt echoes, which generally require accurate calculations of the overlap between the evolved state and the initial wavefunction. By incorporating Clifford disentangling gates during TDVP evolution, our method effectively controls entanglement growth while keeping the computation of these amplitudes accessible. Specifically, it reduces the problem to evaluating the overlap between a Matrix Product State (MPS) and a stabilizer state, a task that remains computationally feasible within the proposed framework. To demonstrate the effectiveness of this approach, we first benchmark it on the one-dimensional transverse-field Ising model. We then apply it to more challenging scenarios, including a non-integrable next-to-nearest-neighbor Ising chain and a two-dimensional Ising model. Our results highlight the versatility and efficiency of the Clifford-augmented MPS, showcasing its capability to go beyond the evaluation of simple expectation values. This makes it a powerful tool for exploring various aspects of many-body quantum dynamics.

Operator-basis Matrix Product State formalism for optical circuits

Authors: Dario Cilluffo, Matthias Kost, Nicola Lorenzoni, Martin B. Plenio

arXiv ID: 2502.01737 | Date: 2025-02-03

Abstract: Tensor network formalisms have emerged as powerful tools for simulating quantum state evolution. While widely applied in the study of optical quantum circuits, such as Boson Sampling, existing tensor network approaches fail to address the complexity mismatch between tensor contractions and the calculation of photon-counting probability amplitudes. Here, we present an alternative tensor network framework, the operator-basis Matrix Product State (MPS), which exploits the input-output relations of quantum optical circuits encoded in the unitary interferometer matrix. Our approach bridges the complexity gap by enabling the computation of the permanent -- central to Boson Sampling -- with the same computational complexity as the best known classical algorithm based on a graphical representation of the operator-basis MPS that we introduce. Furthermore, we exploit the flexibility of tensor networks to extend our formalism to incorporate partial distinguishability and photon loss, two key imperfections in practical interferometry experiments. This work offers a significant step forward in the simulation of large-scale quantum optical systems and the understanding of their computational complexity.

Postselection-free experimental observation of the measurement-induced phase transition in circuits with universal gates

Authors: Xiaozhou Feng, Jeremy Côté, Stefanos Kourtis, Brian Skinner

arXiv ID: 2502.01735 | Date: 2025-02-03

Abstract: Monitored many-body systems can exhibit a phase transition between entangling and disentangling dynamical phases by tuning the strength of measurements made on the system as it evolves. This phenomenon is called the measurement-induced phase transition (MIPT). Understanding the properties of the MIPT is a prominent challenge for both theory and experiment at the intersection of many-body physics and quantum information. Realizing the MIPT experimentally is particularly challenging due to the postselection problem, which demands a number of experimental realizations that grows exponentially with the number of measurements made during the dynamics. Proposed approaches that circumvent the postselection problem typically rely on a classical decoding process that infers the final state based on the measurement record. But the complexity of this classical process generally also grows exponentially with the system size unless the dynamics is restricted to a fine-tuned set of unitary operators. In this work we overcome these difficulties. We construct a tree-shaped quantum circuit whose nodes are Haar-random unitary operators followed by weak measurements of tunable strength. For these circuits, we show that the MIPT can be detected without postselection using only a simple classical decoding process whose complexity grows linearly with the number of qubits. Our protocol exploits the recursive structure of tree circuits, which also enables a complete theoretical description of the MIPT, including an exact solution for its critical point and scaling behavior. We experimentally realize the MIPT on Quantinuum's H1-1 trapped-ion quantum computer and show that the experimental results are precisely described by theory. Our results close the gap between analytical theory and postselection-free experimental observation of the MIPT.

TT-LSQR For Tensor Least Squares Problems and Application to Data Mining *

Authors: Lorenzo Piccinini, Valeria Simoncini

arXiv ID: 2502.01293 | Date: 2025-02-03

Abstract: We are interested in the numerical solution of the tensor least squares problem \[ \min_{\mathcal{X}} \| \mathcal{F} - \sum_{i =1}^{\ell} \mathcal{X} \times_1 A_1^{(i)} \times_2 A_2^{(i)} \cdots \times_d A_d^{(i)} \|_F, \] where XRm1×m2××md\mathcal{X}\in\mathbb{R}^{m_1 \times m_2 \times \cdots \times m_d}, FRn1×n2××nd\mathcal{F}\in\mathbb{R}^{n_1\times n_2 \times \cdots \times n_d} are tensors with dd dimensions, and the coefficients Aj(i)A_j^{(i)} are tall matrices of conforming dimensions. We first describe a tensor implementation of the classical LSQR method by Paige and Saunders, using the tensor-train representation as key ingredient. We also show how to incorporate sketching to lower the computational cost of dealing with the tall matrices Aj(i)A_j^{(i)}. We then use this methodology to address a problem in information retrieval, the classification of a new query document among already categorized documents, according to given keywords.

Generalized Lanczos method for systematic optimization of neural-network quantum states

Authors: Jia-Qi Wang, Rong-Qiang He, Zhong-Yi Lu

arXiv ID: 2502.01264 | Date: 2025-02-03

Abstract: Recently, artificial intelligence for science has made significant inroads into various fields of natural science research. In the field of quantum many-body computation, researchers have developed numerous ground state solvers based on neural-network quantum states (NQSs), achieving ground state energies with accuracy comparable to or surpassing traditional methods such as variational Monte Carlo methods, density matrix renormalization group, and quantum Monte Carlo methods. Here, we combine supervised learning, variational Monte Carlo (VMC), and the Lanczos method to develop a systematic approach to improving the NQSs of many-body systems, which we refer to as the NQS Lanczos method. The algorithm mainly consists of two parts: the supervised learning part and the VMC optimization part. Through supervised learning, the Lanczos states are represented by the NQSs. Through VMC, the NQSs are further optimized. We analyze the reasons for the underfitting problem and demonstrate how the NQS Lanczos method systematically improves the energy in the highly frustrated regime of the two-dimensional Heisenberg J1J_1-J2J_2 model. Compared to the existing method that combines the Lanczos method with the restricted Boltzmann machine, the primary advantage of the NQS Lanczos method is its linearly increasing computational cost.

A Simple and General Equation for Matrix Product Unitary Generation

Authors: Sujeet K. Shukla

arXiv ID: 2502.00390 | Date: 2025-02-01

Abstract: Matrix Product Unitaries (MPUs) have emerged as essential tools for representing locality-preserving 1D unitary operators, with direct applications to quantum cellular automata and quantum phases of matter. A key challenge in the study of MPUs is determining when a given local tensor generates an MPU, a task previously addressed through fixed-point conditions and canonical forms, which can be cumbersome to evaluate for an arbitrary tensor. In this work, we establish a simple and efficient necessary and sufficient condition for a tensor MM to generate an MPU of size NN, given by Tr(EMN)=Tr(ETN)=1\operatorname{Tr}(\mathbb{E}_M^N) = \operatorname{Tr}(\mathbb{E}_T^N) = 1, where EM\mathbb{E}_M and ET\mathbb{E}_T are the transfer matrices of MM and T=MMT = MM^\dagger. This condition provides a unified framework for characterizing all uniform MPUs and significantly simplifies their evaluation. Furthermore, we show that locality preservation naturally arises when the MPU is generated for all system sizes. Our results offer new insights into the structure of MPUs, highlighting connections between unitary evolution, transfer matrices, and locality-preserving behavior, with potential extensions to higher-dimensions.

Semi-group influence matrices for non-equilibrium quantum impurity models

Authors: Michael Sonner, Valentin Link, Dmitry A. Abanin

arXiv ID: 2502.00109 | Date: 2025-01-31

Abstract: We introduce a framework for describing the real-time dynamics of quantum impurity models out of equilibrium which is based on the influence matrix approach. By replacing the dynamical map of a large fermionic quantum environment with an effective semi-group influence matrix (SGIM) which acts on a reduced auxiliary space, we overcome the limitations of previous proposals, achieving high accuracy at long evolution times. This SGIM corresponds to a uniform matrix-product state representation of the influence matrix and can be obtained by an efficient algorithm presented in this paper. We benchmark this approach by computing the spectral function of the single impurity Anderson model with high resolution. Further, the spectrum of the effective dynamical map allows us to obtain relaxation rates of the impurity towards equilibrium following a quantum quench. Finally, for a quantum impurity model with on-site two-fermion loss, we compute the spectral function and confirm the emergence of Kondo physics at large loss rates.

VeloxQ: A Fast and Efficient QUBO Solver

Authors: J. Pawłowski, J. Tuziemski, P. Tarasiuk, A. Przybysz, R. Adamski, K. Hendzel, Ł. Pawela, B. Gardas

arXiv ID: 2501.19221 | Date: 2025-01-31

Abstract: We introduce VeloxQ, a fast and efficient solver for Quadratic Unconstrained Binary Optimization (QUBO) problems, which are central to numerous real-world optimization tasks. Unlike other physics-inspired approaches to optimization problems, such as quantum annealing and quantum computing, VeloxQ does not require substantial progress of technology to unlock its full potential. We benchmark VeloxQ against the state-of-the-art QUBO solvers based on emerging technologies. Our comparison includes quantum annealers, specifically D-Wave's Advantage, and Advantage2 prototype platforms, the digital-quantum algorithm designed to solve Higher-Order Unconstrained Binary Optimization (HUBO) developed by Kipu Quantum, physics-inspired algorithms: Simulated Bifurcation and Parallel Annealing and an algorithm based on tropical tensor networks. We also take into account modern developments of conventional algorithms: Branch and Bound algorithm, an optimal implementation of the brute-force algorithm and BEIT QUBO solver. Our results show that VeloxQ not only matches but often surpasses the mentioned solvers in solution quality and runtime. Additionally, VeloxQ demonstrates excellent scalability being the only solver capable of solving large-scale optimization problems, including up to 2×1082\times 10^{8} sparsely connected variables, that are currently intractable for its competitors. These findings position VeloxQ as a powerful and practical tool for tackling large-scale QUBO and HUBO problems, offering a compelling alternative to existing quantum and classical optimization methods.

Grassmann tensor approach for two-dimensional QCD in the strong-coupling expansion

Authors: Thomas Samberger, Jacques Bloch, Robert Lohmayer

arXiv ID: 2501.19192 | Date: 2025-01-31

Abstract: We present a tensor-network approach for the strong-coupling expansion of two-dimensional QCD with staggered quarks at non-zero chemical potential. After expanding the Boltzmann factor in the gauge and fermion actions, all gauge fields can be integrated out exactly and the partition function can be evaluated using the Grassmann higher-order tensor renormalization group approach. The method is modified to compute the μμ dependence of the quark number density and the chiral condensate up to order β3β^3 with complete absence of higher-order terms infiltrating the result. Although the expansion itself is only a good approximation to the full theory at small β<0.1β<0.1, the range can be extended, by using judiciously chosen fits. Moreover, these fits also yield a valuable expansion in ββ for the critical chemical potential.

A Tensor-Train Decomposition based Compression of LLMs on Group Vector Systolic Accelerator

Authors: Sixiao Huang, Tintin Wang, Ang Li, Ao Shen, Kai Li, Keyao Jiang, Mingqiang Huang, Hao Yu

arXiv ID: 2501.19135 | Date: 2025-01-31

Abstract: Large language models (LLMs) are both storage-intensive and computation-intensive, posing significant challenges when deployed on resource-constrained hardware. As linear layers in LLMs are mainly resource consuming parts, this paper develops a tensor-train decomposition (TTD) for LLMs with a further hardware implementation on FPGA. TTD compression is applied to the linear layers in ChatGLM3-6B and LLaMA2-7B models with compression ratios (CRs) for the whole network 1.94×\times and 1.60×\times, respectively. The compressed LLMs are further implemented on FPGA hardware within a highly efficient group vector systolic array (GVSA) architecture, which has DSP-shared parallel vector PEs for TTD inference, as well as optimized data communication in the accelerator. Experimental results show that the corresponding TTD based LLM accelerator implemented on FPGA achieves 1.45×\times and 1.57×\times reduction in first token delay for ChatGLM3-6B and LLaMA2-7B models, respectively.

Computing theta-dependent mass spectrum of the 2-flavor Schwinger model in the Hamiltonian formalism

Authors: Akira Matsumoto, Etsuko Itou, Yuya Tanizaki

arXiv ID: 2501.18960 | Date: 2025-01-31

Abstract: We compute the θθ-dependent mass spectrum of the 2-flavor Schwingr model using the tensor network (DMRG) in the Hamiltonian formalism. The pion and the sigma meson are identified as stable particles of the model for nonzero θθ whereas the eta meson becomes unstable. The meson masses are obtained from the one-point functions, using the meson operators defined by diagonalizing the correlation matrix to deal with the operator mixing. We also compute the dispersion relation directly by measuring the energy and momentum of the excited states, where the mesons are distinguished by the isospin quantum number. We confirmed that the meson masses computed by these methods agree with each other and are consistent with the calculation by the bosonized model. Our methods are free from the sign problem and show a significant improvement in accuracy compared to the conventional Monte Carlo methods. Furthermore, at the critical point θ=πθ= π, the mesons become almost massless, and the one-point functions reproduce the expected CFT-like behavior.

Two-color lattice QCD in (1+1)(1+1) dimensions with Grassmann tensor renormalization group

Authors: Kwok Ho Pai, Shinichiro Akiyama, Synge Todo

arXiv ID: 2501.18918 | Date: 2025-01-31

Abstract: The (1+1)(1+1)-dimensional two-color lattice QCD is studied with the Grassmann tensor renormalization group. We construct tensor network representations of theories with the staggered fermion and the Wilson fermion and show that Grassmann tensor networks can describe both cases with the same bond dimension. We also propose an efficient initial tensor compression scheme to gauge degrees of freedom. We compute the number density, chiral condensate, and diquark condensate at finite density, employing the staggered fermions. For the theory with Wilson fermion, a critical point in the negative mass region is identified by inspecting the pseudoscalar condensate and the conformal field theory data.

Embedding of Tree Tensor Networks into Shallow Quantum Circuits

Authors: Shota Sugawara, Kazuki Inomata, Tsuyoshi Okubo, Synge Todo

arXiv ID: 2501.18856 | Date: 2025-01-31

Abstract: Variational Quantum Algorithms (VQAs) are being highlighted as key quantum algorithms for demonstrating quantum advantage on Noisy Intermediate-Scale Quantum (NISQ) devices, which are limited to executing shallow quantum circuits because of noise. However, the barren plateau problem, where the gradient of the loss function becomes exponentially small with system size, hinders this goal. Recent studies suggest that embedding tensor networks into quantum circuits and initializing the parameters can avoid the barren plateau. Yet, embedding tensor networks into quantum circuits is generally difficult, and methods have been limited to the simplest structure, Matrix Product States (MPSs). This study proposes a method to embed Tree Tensor Networks (TTNs), characterized by their hierarchical structure, into shallow quantum circuits. TTNs are suitable for representing two-dimensional systems and systems with long-range correlations, which MPSs are inadequate for representing. Our numerical results show that embedding TTNs provides better initial quantum circuits than MPS. Additionally, our method has a practical computational complexity, making it applicable to a wide range of TTNs. This study is expected to extend the application of VQAs to two-dimensional systems and those with long-range correlations, which have been challenging to utilize.

Regularized second-order optimization of tensor-network Born machines

Authors: Matan Ben-Dov, Jing Chen

arXiv ID: 2501.18691 | Date: 2025-01-30

Abstract: Tensor-network Born machines (TNBMs) are quantum-inspired generative models for learning data distributions. Using tensor-network contraction and optimization techniques, the model learns an efficient representation of the target distribution, capable of capturing complex correlations with a compact parameterization. Despite their promise, the optimization of TNBMs presents several challenges. A key bottleneck of TNBMs is the logarithmic nature of the loss function commonly used for this problem. The single-tensor logarithmic optimization problem cannot be solved analytically, necessitating an iterative approach that slows down convergence and increases the risk of getting trapped in one of many non-optimal local minima. In this paper, we present an improved second-order optimization technique for TNBM training, which significantly enhances convergence rates and the quality of the optimized model. Our method employs a modified Newton's method on the manifold of normalized states, incorporating regularization of the loss landscape to mitigate local minima issues. We demonstrate the effectiveness of our approach by training a one-dimensional matrix product state (MPS) on both discrete and continuous datasets, showcasing its advantages in terms of stability and efficiency, and demonstrating its potential as a robust and scalable approach for optimizing quantum-inspired generative models.

Quantum Phase Transitions between Symmetry-Enriched Fracton Phases

Authors: Julian Boesl, Yu-Jie Liu, Wen-Tao Xu, Frank Pollmann, Michael Knap

arXiv ID: 2501.18688 | Date: 2025-01-30

Abstract: Topologically ordered phases exhibit further complexity in the presence of global symmetries: Their anyonic excitations may exhibit different transformation patterns under these symmetries, leading to a classification in terms of symmetry-enriched topological orders. We develop a generic scheme to study an analogous situation for three-dimensional fracton phases by means of isometric tensor network states (isoTNS) with finite bond dimension, which allow us to tune phase transitions between different symmetry fractionalization patterns. We focus on the X-Cube model, a paradigmatic fracton model hosting two types of excitations: lineons, which are mobile in a single direction only, and fractons that are immobile on their own. By deforming the local tensors of the fixed point ground state, we find a family of exact wavefunctions for which the symmetry fractionalization under an anti-unitary symmetry on both types of excitations is directly visible. These wavefunctions are non-stabilizer states and have non-vanishing correlation lengths. They even exhibit power-law correlations at criticality between two symmetry-enriched topological orders. Furthermore, the isoTNS description allows for the explicit construction of a linear-depth quantum circuit to sequentially realize these exotic 3D states on a quantum processor, including a holographic scheme using only a pair of two-dimensional qubit arrays alongside measurements. Our approach provides a construction to enrich phases with exotic topological or fracton order and to study 3D quantum phase transition with exact wavefunctions, and offers a tractable route to implement and characterize fracton order on quantum devices.

Bridging Entanglement and Magic Resources within Operator Space

Authors: Neil Dowling, Kavan Modi, Gregory A. L. White

arXiv ID: 2501.18679 | Date: 2025-01-30

Abstract: Local-operator entanglement (LOE) dictates the complexity of simulating Heisenberg evolution using tensor network methods, {and bears witness to many-body chaos for local dynamics}. We show that LOE is also sensitive to how non-Clifford a unitary is: its magic resources. In particular, we prove that LOE is always upper-bound by three distinct magic monotones: TT-count, unitary nullity, and operator stabilizer Rényi entropy. Moreover, in the average case for large, random circuits, LOE and magic monotones approximately coincide. Our results imply that an operator evolution that is expensive to simulate using tensor network methods must also be inefficient using both stabilizer and Pauli truncation methods. {In terms of a previous conjecture on the characteristic scaling of LOE, our results also mean that non-integrable spin chains cannot be simulated classically}. Entanglement in operator space therefore measures a unified picture of non-classical resources, in stark contrast to the Schrödinger picture.

Probing non-equilibrium topological order on a quantum processor

Authors: M. Will, T. A. Cochran, E. Rosenberg, B. Jobst, N. M Eassa, P. Roushan, M. Knap, A. Gammon-Smith, F. Pollmann

arXiv ID: 2501.18461 | Date: 2025-01-30

Abstract: Out-of-equilibrium phases in many-body systems constitute a new paradigm in quantum matter - they exhibit dynamical properties that may otherwise be forbidden by equilibrium thermodynamics. Among these non-equilibrium phases are periodically driven (Floquet) systems [1-5], which are generically difficult to simulate classically because of their high entanglement. Here we realize a Floquet topologically ordered state theoretically proposed in ref. [6], on an array of superconducting qubits. We image the characteristic dynamics of its chiral edge modes and characterize its emergent anyonic excitations. Devising an interferometric algorithm allows us to introduce and measure a bulk topological invariant to probe the dynamical transmutation of anyons for system sizes up to 58 qubits. Our work demonstrates that quantum processors can provide key insights into the thus-far largely unexplored landscape of highly entangled non-equilibrium phases of matter.

Tensor-network toolbox for probing dynamics of non-Abelian gauge theories

Authors: Emil Mathew, Navya Gupta, Saurabh V. Kadam, Aniruddha Bapat, Jesse Stryker, Zohreh Davoudi, Indrakshi Raychowdhury

arXiv ID: 2501.18301 | Date: 2025-01-30

Abstract: Tensor-network methods enable probing dynamics of strongly interacting quantum many-body systems, including gauge theories, via Hamiltonian simulation, hence bypassing sign problems. They also have the potential to inform efficient quantum-simulation algorithms of the same theories. We develop and benchmark a matrix-product-state ansatz for the SU(2) lattice gauge theory using the loop-string-hadron formulation. This formulation has been demonstrated to be advantageous in Hamiltonian simulation of non-Abelian gauge theories. It is applicable to both SU(2) and SU(3) gauge groups, to periodic and open boundary conditions, and to 1+1 and higher dimensions. In this work, we report on progress in computing static and dynamical observables in a SU(2) gauge theory in (1+1)D, pushing the boundary of existing studies.

Tensor network state methods and quantum information theory for strongly correlated molecular systems

Authors: Miklós Antal Werner, Andor Menczer, Örs Legeza

arXiv ID: 2501.18263 | Date: 2025-01-30

Abstract: A brief pedagogical overview of recent advances in tensor network state methods are presented that have the potential to broaden their scope of application radically for strongly correlated molecular systems. These include global fermionic mode optimization, i.e., a general approach to find an optimal matrix product state (MPS) parametrization of a quantum many-body wave function with the minimum number of parameters for a given error margin, the restricted active space DMRG-RAS-X method, multi-orbital correlations and entanglement, developments on hybrid CPU-multiGPU parallelization, and an efficient treatment of non-Abelian symmetries on high-performance computing (HPC) infrastructures. Scaling analysis on NVIDIA DGX-A100 platform is also presented.

Realization of Two-dimensional Discrete Time Crystals with Anisotropic Heisenberg Coupling

Authors: Eric D. Switzer, Niall Robertson, Nathan Keenan, Ángel Rodríguez, Andrea D'Urbano, Bibek Pokharel, Talat S. Rahman, Oles Shtanko, Sergiy Zhuk, Nicolás Lorente

arXiv ID: 2501.18036 | Date: 2025-01-29

Abstract: A discrete time crystal (DTC) is the paradigmatic example of a phase of matter that occurs exclusively in systems out of equilibrium. This phenomenon is characterized by the spontaneous symmetry breaking of discrete time-translation and provides a rich playground to study a fundamental question in statistical physics: what mechanism allows for driven quantum systems to exhibit emergent behavior that deviates from their counterparts with time-independent evolution? Unlike equilibrium phases, DTCs exhibit macroscopic manifestations of coherent quantum dynamics, challenging the conventional narrative that thermodynamic behavior universally erases quantum signatures. However, due to the difficulty of simulating these systems with either classical or quantum computers, previous studies have been limited to a set of models with Ising-like couplings -- and mostly only in one dimension -- thus precluding our understanding of the existence (or not) of DTCs in models with interactions that closely align with what occurs in nature. In this work, by combining the latest generation of IBM quantum processors with state-of-the-art tensor network methods, we are able to demonstrate the existence of a DTC in a two-dimensional system governed by anisotropic Heisenberg interactions. Our comprehensive analysis reveals a rich phase diagram encompassing spin-glass, ergodic, and time-crystalline phases, highlighting the tunability of these phases through multiple control parameters. Crucially, our results emphasize the interplay of initialization, interaction anisotropy, and driving protocols in stabilizing the DTC phase. By extending the study of Floquet matter beyond simplified models, we lay the groundwork for exploring how driven systems bridge the gap between quantum coherence and emergent non-equilibrium thermodynamics.

String Breaking in a 2+12+1D Z2\mathbb{Z}_2 Lattice Gauge Theory

Authors: Umberto Borla, Jesse J. Osborne, Sergej Moroz, Jad C. Halimeh

arXiv ID: 2501.17929 | Date: 2025-01-29

Abstract: String breaking is an intriguing phenomenon crucial to the understanding of lattice gauge theories (LGTs), with strong relevance to both condensed matter and high-energy physics (HEP). Recent experiments investigating string breaking in 2+12+1D (two spatial and one temporal dimensions) LGTs motivate a thorough analysis of its underlying mechanisms. Here, we perform matrix product state (MPS) simulations of string breaking in an experimentally relevant 2+12+1D Z2\mathbb{Z}_2 LGT in the presence of two external charges. We provide a detailed description of the system in the confined phase, highlight a number of mechanisms which are responsible for string breaking, and argue that magnetic fluctuations have a stabilizing effect on the strings. Moreover, we show that deep in the confined regime the problem is dual to one-dimensional free fermions hopping on an open chain. Our work elucidates the microscopic processes of string breaking in 2+12+1D LGTs, and our findings can be probed on current superconducting-qubit quantum computers.

Large-scale stochastic simulation of open quantum systems

Authors: Aaron Sander, Maximilian Fröhlich, Martin Eigel, Jens Eisert, Patrick Gelß, Michael Hintermüller, Richard M. Milbradt, Robert Wille, Christian B. Mendl

arXiv ID: 2501.17913 | Date: 2025-01-29

Abstract: Understanding the precise interaction mechanisms between quantum systems and their environment is crucial for advancing stable quantum technologies, designing reliable experimental frameworks, and building accurate models of real-world phenomena. However, simulating open quantum systems, which feature complex non-unitary dynamics, poses significant computational challenges that require innovative methods to overcome. In this work, we introduce the tensor jump method (TJM), a scalable, embarrassingly parallel algorithm for stochastically simulating large-scale open quantum systems, specifically Markovian dynamics captured by Lindbladians. This method is built on three core principles where, in particular, we extend the Monte Carlo wave function (MCWF) method to matrix product states, use a dynamic time-dependent variational principle (TDVP) to significantly reduce errors during time evolution, and introduce what we call a sampling MPS to drastically reduce the dependence on the simulation's time step size. We demonstrate that this method scales more effectively than previous methods and ensures convergence to the Lindbladian solution independent of system size, which we show both rigorously and numerically. Finally, we provide evidence of its utility by simulating Lindbladian dynamics of XXX Heisenberg models up to a thousand spins using a consumer-grade CPU. This work represents a significant step forward in the simulation of large-scale open quantum systems, with the potential to enable discoveries across various domains of quantum physics, particularly those where the environment plays a fundamental role, and to both dequantize and facilitate the development of more stable quantum hardware.

System-environmental entanglement in critical spin systems under ZZZZ-decoherence and its relation to strong and weak symmetries

Authors: Yoshihito Kuno, Takahiro Orito, Ikuo Ichinose

arXiv ID: 2501.17481 | Date: 2025-01-29

Abstract: Open quantum many-body systems exhibit nontrivial behavior under decoherence. In particular, system-environmental entanglement (SEE) is one of the efficient quantities for classifying mixed states subject to decoherence. In this work, we investigate the SEE of critical spin chains under nearest-neighbor ZZZZ-decoherence. We numerically show that the SEE exhibits a specific scaling law, in particular, its system-size-independent term (``gg-function'') changes drastically its behavior in the vicinity of phase transition caused by decoherence. For the XXZ model in its gapless regime, a transition diagnosed by strong Rényi-2 correlations occurs as the strength of the decoherence increases. We determine the location of the phase transition by investigating the gg-function that exhibits a sharp change in the critical region of the transition. Furthermore, we find that the value of the SEE is twice that of the system under single-site ZZ-decoherence, which was recently studied by conformal field theory. From the viewpoint of Rényi-2 Shannon entropy}, which is closely related to the SEE at the maximal decoherence, we clarify the origin of this gg-function behavior.

Linear-time classical approximate optimization of cubic-lattice classical spin glasses: upper bounds on optimality gaps of quantum speedups

Authors: Adil A. Gangat

arXiv ID: 2501.17267 | Date: 2025-01-28

Abstract: Demonstrating quantum speedup for approximate optimization of classical spin glasses is of current interest. Such a demonstration must be done with respect to the best-known scaling of classical heuristics at a given optimality gap of a given problem. For cubic-lattice classical Ising spin glasses, recent theoretical and experimental developments open the possibility of showing quantum speedup for approximate optimization with quantum annealing. It is therefore desirable to understand the optimality-gap range over which such a speedup should be searched for. Here we show that on cubic-lattice tile-planting models, classical meta-heuristics that are linear-time by construction can reach optimality gaps at which simulated annealing and parallel tempering exhibit super-linear scaling. This implies that the optimality gaps achieved by linear-time classical meta-heuristics can serve as useful upper bounds for the optimality-gap range over which quantum speedups in approximate optimization should be searched for. We also explain how classical heuristics with fixed scaling that is beyond-cubic can provide upper bounds to optimality-gap ranges for beyond-quadratic quantum speedups in approximate optimization. These results encourage the development of classical heuristics with fixed scaling that achieve optimality gaps as small as possible.

Approximation of High-Dimensional Gibbs Distributions with Functional Hierarchical Tensors

Authors: Nan Sheng, Xun Tang, Haoxuan Chen, Lexing Ying

arXiv ID: 2501.17143 | Date: 2025-01-28

Abstract: The numerical representation of high-dimensional Gibbs distributions is challenging due to the curse of dimensionality manifesting through the intractable normalization constant calculations. This work addresses this challenge by performing a particle-based high-dimensional parametric density estimation subroutine, and the input to the subroutine is Gibbs samples generated by leveraging advanced sampling techniques. Specifically, to generate Gibbs samples, we employ ensemble-based annealed importance sampling, a population-based approach for sampling multimodal distributions. These samples are then processed using functional hierarchical tensor sketching, a tensor-network-based density estimation method for high-dimensional distributions, to obtain the numerical representation of the Gibbs distribution. We successfully apply the proposed approach to complex Ginzburg-Landau models with hundreds of variables. In particular, we show that the approach proposed is successful at addressing the metastability issue under difficult numerical cases.

MPS Stability and the Intersection Property

Authors: José Garre-Rubio, Alex Turzillo, András Molnár

arXiv ID: 2501.17109 | Date: 2025-01-28

Abstract: We identify a property of the local tensors of matrix product states (MPS) that guarantees that their parent Hamiltonians satisfy the intersection property. The intersection property ensures that the ground space consists of MPS, with degeneracy bounded by the square of the bond dimension. The new local property, dubbed stability, generalizes (block) injectivity and is satisfied by the MPS tensors that construct the W state, domain wall superposition states, and their generalizations.

Two Channel Kondo behavior in the quantum XX chain with a boundary defect

Authors: Yicheng Tang, Pradip Kattel, J. H. Pixley, Natan Andrei

arXiv ID: 2501.16415 | Date: 2025-01-27

Abstract: We demonstrate that a boundary defect in the single spin-12\frac{1}{2} quantum XXXX chain exhibits two-channel Kondo physics. Due to the presence of the defect, the edge spin fractionalizes into two Majorana fermions, out of which one decouples, and one is overscreened by the free fermion in bulk, leading to non-trivial boundary behavior characteristic of the two-channel Kondo model. When the ratio of boundary to bulk coupling exceeds a critical value of 2\sqrt{2}, a massive boundary-bound mode is exponentially localized near the impurity site for strong impurity coupling. This leads to unusual behavior in physical quantities, such as the gg-function not being monotonic. We compute the gg-function of the impurity from both thermodynamic and entanglement entropy calculations and show that it takes a non-integer value of 2\sqrt{2} just as in the two-channel Kondo problem.

Twisted gauging and topological sectors in (2+1)d abelian lattice gauge theories

Authors: Bram Vancraeynest-De Cuiper, Clement Delcamp

arXiv ID: 2501.16301 | Date: 2025-01-27

Abstract: Given a two-dimensional quantum lattice model with an abelian gauge theory interpretation, we investigate a duality operation that amounts to gauging its invertible 1-form symmetry, followed by gauging the resulting 0-form symmetry in a twisted way via a choice of discrete torsion. Using tensor networks, we introduce explicit lattice realisations of the so-called condensation defects, which are obtained by gauging the 1-form symmetry along submanifolds of spacetime, and employ the same calculus to realise the duality operators. By leveraging these tensor network operators, we compute the non-trivial interplay between symmetry-twisted boundary conditions and charge sectors under the duality operation, enabling us to construct isometries relating the dual Hamiltonians. Whenever a lattice gauge theory is left invariant under the duality operation, we explore the possibility of promoting the self-duality to an internal symmetry. We argue that this results in a symmetry structure that encodes the 2-representations of a 2-group.

Strongly correlated states of transition metal spin defects: the case of an iron impurity in aluminum nitride

Authors: Leon Otis, Yu Jin, Victor Wen-zhe Yu, Siyuan Chen, Laura Gagliardi, Giulia Galli

arXiv ID: 2501.16280 | Date: 2025-01-27

Abstract: We investigate the electronic properties of an exemplar transition metal impurity in an insulator, with the goal of accurately describing strongly correlated, defect states. We consider iron in aluminum nitride, a material of interest for hybrid quantum technologies, and we carry out calculations with quantum embedding methods -- density matrix embedding theory (DMET) and quantum defect embedding theory (QDET) and with spin-flip time-dependent density functional theory (TDDFT). We show that both DMET and QDET accurately describe the ground state and low-lying excited states of the defect, and that TDDFT yields photoluminescence spectra in agreement with experiments. In addition, we provide a detailed discussion of the convergence of our results as a function of the active space used in the embedding methods, thus defining a protocol to obtain converged data, directly comparable with experiments.

Harnessing CUDA-Q's MPS for Tensor Network Simulations of Large-Scale Quantum Circuits

Authors: Gabin Schieffer, Stefano Markidis, Ivy Peng

arXiv ID: 2501.15939 | Date: 2025-01-27

Abstract: Quantum computer simulators are an indispensable tool for prototyping quantum algorithms and verifying the functioning of existing quantum computer hardware. The current largest quantum computers feature more than one thousand qubits, challenging their classical simulators. State-vector quantum simulators are challenged by the exponential increase of representable quantum states with respect to the number of qubits, making more than fifty qubits practically unfeasible. A more appealing approach for simulating quantum computers is adopting the tensor network approach, whose memory requirements fundamentally depend on the level of entanglement in the quantum circuit, and allows simulating the current largest quantum computers. This work investigates and evaluates the CUDA-Q tensor network simulators on an Nvidia Grace Hopper system, particularly the Matrix Product State (MPS) formulation. We compare the performance of the CUDA-Q state vector implementation and validate the correctness of MPS simulations. Our results highlight that tensor network-based methods provide a significant opportunity to simulate large-qubit circuits, albeit approximately. We also show that current GPU-accelerated computation cannot fully utilize GPU efficiently in the case of MPS simulations.

Improving accuracy of tree-tensor network approach by optimization of network structure

Authors: Toshiya Hikihara, Hiroshi Ueda, Kouichi Okunishi, Kenji Harada, Tomotoshi Nishino

arXiv ID: 2501.15514 | Date: 2025-01-26

Abstract: Numerical methods based on tensor networks have been extensively explored in the research of quantum many-body systems in recent years. It has been recognized that the ability of tensor networks to describe a quantum many-body state crucially depends on the spatial structure of the network. In the previous work [Hikihara et al., Phys. Rev. Res. 5, 013031 (2023)], we proposed an algorithm based on tree tensor networks (TTNs) that automatically optimizes the structure of TTN according to the spatial profile of entanglement in the state of interest. In this paper, we apply the algorithm to the random XY-exchange model under random magnetic fields and the Richardson model in order to analyze how the performance of the algorithm depends on the detailed updating schemes of the structural optimization. We then find that for the random XY model, on the one hand, the algorithm achieves improved accuracy, and the stochastic algorithm, which selects the local network structure probabilistically, is notably effective. For the Richardson model, on the other hand, the resulting numerical accuracy subtly depends on the initial TTN and the updating schemes. In particular, the algorithm without the stochastic updating scheme certainly improves the accuracy, while the one with the stochastic updates results in poor accuracy due to the effect of randomizing the network structure at the early stage of the calculation. These results indicate that the algorithm successfully improves the accuracy of the numerical calculations for quantum many-body states, while it is essential to appropriately choose the updating scheme as well as the initial TTN structure, depending on the systems treated.

Transverse Field Dependence of the Ground State in the Z2 Bose-Hubbard Model

Authors: Yuma Watanabe, Shohei Watabe, Tetsuro Nikuni

arXiv ID: 2501.15490 | Date: 2025-01-26

Abstract: The study of interaction between the particle and lattice degrees of freedom is one of the central interests in the quantum many-body systems. The Z2 Bose-Hubbard model has been proposed to describe ultracold bosons in a dynamical optical lattice. This model introduces the lattice degrees of freedom by placing half-spins on the bonds between neighboring lattice sites. In this study, we investigate the effect of spin fluctuations on the ground state by using the density-matrix renormalization group method. By calculating the spin structure factor and the compressibility, we show that there is a phase transition between two spatially nonuniform states. We also discuss the ground state in the strong transverse magnetic field.

Tensor renormalization group study of the two-dimensional lattice U(1) gauge-Higgs model with a topological θθ term under Lüscher's admissibility condition

Authors: Shinichiro Akiyama, Yoshinobu Kuramashi

arXiv ID: 2501.15352 | Date: 2025-01-26

Abstract: We investigate the two-dimensional lattice U(1) gauge-Higgs model with a topological term, employing Lüscher's admissibility condition. The standard Monte Carlo simulation for this model is hindered not only by the complex action problem due to the topological term but also by the topological freezing problem originating from the admissibility condition. Resolving both obstacles simultaneously with the tensor renormalization group approach, we show the advantage of the admissibility condition in dealing with the topological term discretized with the so-called field-theoretical definition.

Dualities between 2+1d fusion surface models from braided fusion categories

Authors: Luisa Eck

arXiv ID: 2501.14722 | Date: 2025-01-24

Abstract: Fusion surface models generalize the concept of anyon chains to 2+1 dimensions, utilizing fusion 2-categories as their input. We investigate bond-algebraic dualities in these systems and show that distinct module tensor categories M\mathcal{M} over the same braided fusion category B\mathcal{B} give rise to dual lattice models. This extends the 1+1d result that dualities in anyon chains are classified by module categories over fusion categories. We analyze two concrete examples: (i) a Rep(S3)\text{Rep}(S_3) model with a constrained Hilbert space, dual to the spin-12\tfrac{1}{2} XXZ model on the honeycomb lattice, and (ii) a bilayer Kitaev honeycomb model, dual to a spin-12\tfrac{1}{2} model with XXZ and Ising interactions. Unlike regular M=B\mathcal{M}=\mathcal{B} fusion surface models, which conserve only 1-form symmetries, models constructed from MB\mathcal{M} \neq \mathcal{B} can exhibit both 1-form and 0-form symmetries, including non-invertible ones.

Bipartite Fluctuations and Charge Fractionalization in Quantum Wires

Authors: Magali Korolev, Karyn Le Hur

arXiv ID: 2501.14410 | Date: 2025-01-24

Abstract: We introduce a quantum information method for measuring fractional charges in ballistic quantum wires generalizing bipartite fluctuations to the chiral quasiparticles in Luttinger liquids, i.e. adding charge and current fluctuations in a region of the wire. Bipartite fluctuations at equilibrium are characterized through a logarithmic scaling with distance encoding the entangled nature of these fractional charges in one-dimensional (1D) fluids. This approach clarifies the physical meaning of the dephasing factor of electronic interferences in a ballistic ring geometry at zero temperature, as a result of charge fractionalization. We formulate an analogy towards ground-state energetics. We show how bipartite current fluctuations represent a useful tool to locate quantum phase transitions associated to Mott physics. We address a spin chain equivalence and verify the fractional charges through an algorithm such as Density Matrix Renormalization Group (DMRG). Adding a potential difference between the two sides (parties) of the wire, bipartite fluctuations can detect a bound state localized at the interface through the Jackiw-Rebbi model coexisting with fractional charges.

Toward tensor renormalization group study of lattice QCD

Authors: Atis Yosprakob

arXiv ID: 2501.14293 | Date: 2025-01-24

Abstract: The tensor renormalization group is a promising complementary approach to traditional Monte Carlo methods for lattice systems, as it is inherently free from the sign problem. We discuss recent developments crucial for its application to lattice QCD: the multi-layer construction for multi-flavor gauge theory and the armillary sphere formulation for non-Abelian gauge theory. These techniques are important for reducing the size of the initial tensor and for eliminating non-local entanglement structures within the tensor network. We present selected numerical results and discuss potential generalizations to lattice QCD.

A Classifying Space for Phases of Matrix Product States

Authors: Agnes Beaudry, Michael Hermele, Markus J. Pflaum, Marvin Qi, Daniel D. Spiegel, David T. Stephen

arXiv ID: 2501.14241 | Date: 2025-01-24

Abstract: We construct a topological space B\mathcal{B} consisting of translation invariant injective matrix product states (MPS) of all physical and bond dimensions and show that it has the weak homotopy type K(Z,2)×K(Z,3)K(\mathbb{Z}, 2) \times K(\mathbb{Z}, 3). The implication is that the phase of a family of such states parametrized by a space XX is completely determined by two invariants: a class in H2(X;Z)H^2(X; \mathbb{Z}) corresponding to the Chern number per unit cell and a class in H3(X;Z)H^3(X; \mathbb{Z}), the so-called Kapustin-Spodyneiko (KS) number. The space B\mathcal{B} is defined as the quotient of a contractible space E\mathcal{E} of MPS tensors by an equivalence relation describing gauge transformations of the tensors. We prove that the projection map p:EBp:\mathcal{E} \rightarrow \mathcal{B} is a quasifibration, and this allows us to determine the weak homotopy type of B\mathcal{B}. As an example, we review the Chern number pump-a family of MPS parametrized by S3S^3-and prove that it generates π3(B)π_3(\mathcal{B}).

Grassmann Tensor Renormalization Group for two-flavor massive Schwinger model with a theta term

Authors: Hayato Kanno, Shinichiro Akiyama, Kotaro Murakami, Shinji Takeda

arXiv ID: 2501.14086 | Date: 2025-01-23

Abstract: We investigate the Nf=2N_f=2 Schwinger model with the massive staggered fermions in the presence of a 2π periodic θθ term, using the Grassmann tensor renormalization group. Thanks to the Grassmann tensor network formulation, there is no difficulty in dealing with the massive staggered fermions. We study the θθ dependence of the free energy in the thermodynamic limit. Our calculation provides consistent results with the analytical solution in the large mass limit. The results also suggest that the Nf=2N_f=2 Schwinger model on a lattice has a different phase structure from that described by the continuum theory.

Meson thermalization with a hot medium in the open Schwinger model

Authors: Takis Angelides, Yibin Guo, Karl Jansen, Stefan Kühn, Giuseppe Magnifico

arXiv ID: 2501.13675 | Date: 2025-01-23

Abstract: Quantum field theories treated as open quantum systems provide a crucial framework for studying realistic experimental scenarios, such as quarkonia traversing the quark-gluon plasma produced at the Large Hadron Collider. In such cases, capturing the complex thermalization process requires a detailed understanding of how particles evolve and interact with a hot medium. Considering the open lattice Schwinger model and using tensor network algorithms, we investigate the thermalization dynamics of mesonic particles in a hot medium, such as the Schwinger boson or the electric flux string. We simulate systems with up to 100 lattice sites, achieving accurate preservation of the electric field parity symmetry, demonstrating the algorithm's robustness and scalability. Our results reveal that the thermalization time increases with stronger dissipation from the environment, increasing environment temperature, higher background electric field and heavier fermion masses. Further, we study the quantum mutual information between the two halves of the flux string connecting a meson's constituent particles and analyze its relation to relevant dynamical observables.

Fast and Provable Tensor-Train Format Tensor Completion via Precondtioned Riemannian Gradient Descent

Authors: Fengmiao Bian, Jian-Feng Cai, Xiaoqun Zhang, Yuanwei Zhang

arXiv ID: 2501.13385 | Date: 2025-01-23

Abstract: Low-rank tensor completion aims to recover a tensor from partially observed entries, and it is widely applicable in fields such as quantum computing and image processing. Due to the significant advantages of the tensor train (TT) format in handling structured high-order tensors, this paper investigates the low-rank tensor completion problem based on the TT-format. We proposed a preconditioned Riemannian gradient descent algorithm (PRGD) to solve low TT-rank tensor completion and establish its linear convergence. Experimental results on both simulated and real datasets demonstrate the effectiveness of the PRGD algorithm. On the simulated dataset, the PRGD algorithm reduced the computation time by two orders of magnitude compared to existing classical algorithms. In practical applications such as hyperspectral image completion and quantum state tomography, the PRGD algorithm significantly reduced the number of iterations, thereby substantially reducing the computational time.

Non-zero noise extrapolation: accurately simulating noisy quantum circuits with tensor networks

Authors: Anthony P. Thompson, Arie Soeteman, Chris Cade, Ido Niesen

arXiv ID: 2501.13237 | Date: 2025-01-22

Abstract: Understanding the effects of noise on quantum computations is fundamental to the development of quantum hardware and quantum algorithms. Simulation tools are essential for quantitatively modelling these effects, yet unless artificial restrictions are placed on the circuit or noise model, accurately modelling noisy quantum computations is an extremely challenging task due to unfavourable scaling of required computational resources. Tensor network methods offer a viable solution for simulating computations that generate limited entanglement or that have noise models which yield low gate fidelities. However, in the most interesting regime of entangling circuits (with high gate fidelities) relevant for error correction and mitigation tensor network simulations often achieve poor accuracy. In this work we develop and numerically test a method for significantly improving the accuracy of tensor network simulations of noisy quantum circuits in the low-noise (i.e. high gate-fidelity) regime. Our method comes with the advantages that it (i) allows for the simulation of quantum circuits under generic types of noise model, (ii) is especially tailored to the low-noise regime, and (iii) retains the benefits of tensor network scaling, enabling efficient simulations of large numbers of qubits. We build upon the observations that adding extra noise to a quantum circuit makes it easier to simulate with tensor networks, and that the results can later be reliably extrapolated back to the low-noise regime of interest. These observations form the basis for a novel emulation technique that we call non-zero noise extrapolation, in analogy to the quantum error mitigation technique of zero-noise extrapolation.

Random Quantum Circuits with Time-Reversal Symmetry

Authors: Kabir Khanna, Abhishek Kumar, Romain Vasseur, Andreas W. W. Ludwig

arXiv ID: 2501.13161 | Date: 2025-01-22

Abstract: Time-reversal (TR) symmetry is crucial for understanding a wide range of physical phenomena, and plays a key role in constraining fundamental particle interactions and in classifying phases of quantum matter. In this work, we introduce an ensemble of random quantum circuits that are representative of the dynamics of generic TR-invariant many-body quantum systems. We derive a general statistical mechanics model describing entanglement, many-body quantum chaos and quantum information dynamics in such TR-invariant circuits. As an example of application of our formalism, we study the universal properties of measurement-induced phase transitions (MIPT) in monitored TR-invariant systems, with measurements performed in a TR-invariant basis. We find that TR-invariance of the unitary part of the dynamics does not affect the universality class, unless measurement outcomes are post-selected to satisfy the global TR-invariance of each quantum trajectory. We confirm these predictions numerically, and find, for both generic and Clifford-based evolutions, novel critical exponents in the case of ``strong'', i.e. global TR-invariance where each quantum trajectory is TR-invariant.

Bound states and deconfined spinons in the dynamical structure factor of the J1J2J_1 - J_2 spin-1 chain

Authors: Aman Sharma, Mithilesh Nayak, Henrik M. Rønnow, Frédéric Mila

arXiv ID: 2501.13059 | Date: 2025-01-22

Abstract: Using a time-dependent density matrix renormalization group approach, we study the dynamical structure factor of the J1J2J_1 - J_2 spin-1 chain. As J2J_2 increases, the magnon mode develops incommensurability. The system undergoes a first-order transition at J2=0.76J1J_2 = 0.76 J_1, and at that point, domain walls lead to a continuum of fractional quasi-particles or spinons. By studying small variations in J2J_2 around the transition point, we observe the confinement of spinons into bound states in the spectral function and find a smooth evolution of the spectrum into magnon modes away from the phase transition. We employ the single-mode approximation to accurately account for the dispersion of the magnon mode away from the phase transition and describe the associated continua and bound states. We extend the single-mode approximation to describe the dispersion of a spinon at the phase transition point and obtain its dispersion throughout the Brillouin zone. This allows us to relate the incommensurability at and around the transition point to the competition between a negative nearest-neighbour hopping amplitude and a positive next-nearest-neighbour one for the domain wall.

Tensor cross interpolation approach for quantum impurity problems based on the weak-coupling expansion

Authors: Shuta Matsuura, Hiroshi Shinaoka, Philipp Werner, Naoto Tsuji

arXiv ID: 2501.12643 | Date: 2025-01-22

Abstract: We apply the tensor cross interpolation (TCI) algorithm to solve equilibrium quantum impurity problems with high precision based on the weak-coupling expansion. The TCI algorithm, a kind of active learning method, factorizes high-dimensional integrals that appear in the perturbative expansion into a product of low-dimensional ones, enabling us to evaluate higher-order terms efficiently. This method is free from the sign problem which quantum Monte Carlo methods sometimes suffer from, and allows one to directly calculate the free energy. We benchmark the TCI impurity solver on an exactly solvable impurity model, and find good agreement with the exact solutions. We also incorporate the TCI impurity solver into the dynamical mean-field theory to solve the Hubbard model, and show that the metal-to-Mott insulator transition is correctly described with comparable accuracy to the Monte Carlo methods. Behind the effectiveness of the TCI approach for quantum impurity problems lies the fact that the integrands in the weak-coupling expansion naturally have a low-rank structure in the tensor-train representation.

Classical and quantum algorithms for characters of the symmetric group

Authors: Sergey Bravyi, David Gosset, Vojtech Havlicek, Louis Schatzki

arXiv ID: 2501.12579 | Date: 2025-01-22

Abstract: Characters of irreducible representations are ubiquitous in group theory. However, computing characters of some groups such as the symmetric group SnS_n is a challenging problem known to be #P\#P-hard in the worst case. Here we describe a Matrix Product State (MPS) algorithm for characters of SnS_n. The algorithm computes an MPS encoding all irreducible characters of a given permutation. It relies on a mapping from characters of SnS_n to quantum spin chains proposed by Crichigno and Prakash. We also provide a simpler derivation of this mapping. We complement this result by presenting a poly(n)poly(n) size quantum circuit that prepares the corresponding MPS, obtaining an efficient quantum algorithm for certain sampling problems based on characters of SnS_n. To assess classical hardness of these problems we present a general reduction from strong simulation (computing a given probability) to weak simulation (sampling with a small error). This reduction applies to any sampling problem with a certain granularity structure and may be of independent interest.

Entanglement asymmetry dynamics in random quantum circuits

Authors: Filiberto Ares, Sara Murciano, Pasquale Calabrese, Lorenzo Piroli

arXiv ID: 2501.12459 | Date: 2025-01-21

Abstract: We study the dynamics of entanglement asymmetry in random unitary circuits (RUCs). Focusing on a local U(1)U(1) charge, we consider symmetric initial states evolved by both local one-dimensional circuits and geometrically non-local RUCs made of two-qudit gates. We compute the entanglement asymmetry of subsystems of arbitrary size, analyzing the relaxation time scales. We show that the entanglement asymmetry of the whole system approaches its stationary value in a time independent of the system size for both local and non-local circuits. For subsystems, we find qualitative differences depending on their size. When the subsystem is larger than half of the full system, the equilibration time scales are again independent of the system size for both local and non-local circuits and the entanglement asymmetry grows monotonically in time. Conversely, when the subsystems are smaller than half of the full system, we show that the entanglement asymmetry is non-monotonic in time and that it equilibrates in a time proportional to the quantum-information scrambling time, providing a physical intuition. As a consequence, the subsystem-equilibration time depends on the locality of interactions, scaling linearly and logarithmically in the system size, respectively, for local and non-local RUCs. Our work confirms the entanglement asymmetry as a versatile and computable probe of symmetry in many-body physics and yields a phenomenological overview of entanglement-asymmetry evolution in typical non-integrable dynamics.

Quantum Compressive Sensing Meets Quantum Noise: A Practical Exploration

Authors: Naveed Naimipour, Collin Frink, Harry Shaw, Haleh Safavi, Mojtaba Soltanalian

arXiv ID: 2501.12335 | Date: 2025-01-21

Abstract: Compressive sensing is a signal processing technique that enables the reconstruction of sparse signals from a limited number of measurements, leveraging the signal's inherent sparsity to facilitate efficient recovery. Recent works on the Quantum Compressive Sensing (QCS) architecture, a quantum data-driven approach to compressive sensing where the state of the tensor network is represented by a quantum state over a set of entangled qubits, have shown promise in advancing quantum data-driven methods for compressive sensing. However, the QCS framework has remained largely untested on quantum computing resources or in the presence of quantum noise. In this work, we present a practical implementation of QCS on Amazon Braket, utilizing the Quantum Imaginary Time Evolution (QITE) projection technique to assess the framework's capabilities under quantum noise. We outline the necessary modifications to the QCS framework for deployment on Amazon Braket, followed by results under four types of quantum noise. Finally, we discuss potential long-term directions aimed at unlocking the full potential of quantum compressive sensing for applications such as signal recovery and image processing.

Reply to comment on "Controlled bond expansion for Density Matrix Renormalization Group ground state search at single-site costs"

Authors: Andreas Gleis, Jheng-Wei Li, Jan von Delft

arXiv ID: 2501.12291 | Date: 2025-01-21

Abstract: We reply to McCulloch and Osborne's recent comment on our manuscript (Phys. Rev. Lett. 130, 246402 (2023)) on controlled bond expansion (CBE) for density matrix renormalization group (DMRG) ground state search. We appreciate their suggestion to consider randomized SVD and address their constructive critique on the variational properties of CBE-DMRG. However, we strongly disagree with their proposal to omit the projection to the 2-site tangent space and explain its importance for efficient bond expansion. In particular, in the context of CBE applied to the time-dependent variational principle (TDVP), we show that omitting this projection can lead to avoidable errors. Lastly, we emphasize the complementary roles of 3S mixing and CBE, reiterating our recommendation from Phys. Rev. Lett. 130, 246402 (2023) to combine both methods (CBE+αα). We provide examples to demonstrate the superior efficiency and robustness of CBE+αα.

Quantum-Inspired Solver for Simulating Material Deformations

Authors: Mazen Ali, Aser Cortines, Siddhartha Morales, Samuel Mugel, Mireia Olave, Roman Orus, Samuel Palmer, Hodei Usabiaga

arXiv ID: 2501.12151 | Date: 2025-01-21

Abstract: This paper explores the application of tensor networks (TNs) to the simulation of material deformations within the framework of linear elasticity. Material simulations are essential computational tools extensively used in both academic research and industrial applications. TNs, originally developed in quantum mechanics, have recently shown promise in solving partial differential equations (PDEs) due to their potential for exponential speedups over classical algorithms. Our study successfully employs TNs to solve linear elasticity equations with billions of degrees of freedom, achieving exponential reductions in both memory usage and computational time. These results demonstrate the practical viability of TNs as a powerful classical backend for executing quantum-inspired algorithms with significant efficiency gains. This work is based on our research conducted with IKERLAN.

Regularized dynamical parametric approximation of stiff evolution problems

Authors: Christian Lubich, Jörg Nick

arXiv ID: 2501.12118 | Date: 2025-01-21

Abstract: Evolutionary deep neural networks have emerged as a rapidly growing field of research. This paper studies numerical integrators for such and other classes of nonlinear parametrizations u(t)=Φ(θ(t))u(t) = Φ(θ(t)), where the evolving parameters θ(t)θ(t) are to be computed. The primary focus is on tackling the challenges posed by the combination of stiff evolution problems and irregular parametrizations, which typically arise with neural networks, tensor networks, flocks of evolving Gaussians, and in further cases of overparametrization. We propose and analyse regularized parametric versions of the implicit Euler method and higher-order implicit Runge--Kutta methods for the time integration of the parameters in nonlinear approximations to evolutionary partial differential equations and large systems of stiff ordinary differential equations. At each time step, an ill-conditioned nonlinear optimization problem is solved approximately with a few regularized Gauss--Newton iterations. Error bounds for the resulting parametric integrator are derived by relating the computationally accessible Gauss--Newton iteration for the parameters to the computationally inaccessible Newton iteration for the underlying non-parametric time integration scheme. The theoretical findings are supported by numerical experiments that are designed to show key properties of the proposed parametric integrators.

Initial tensor construction for the tensor renormalization group

Authors: Katsumasa Nakayama, Manuel Schneider

arXiv ID: 2501.11810 | Date: 2025-01-21

Abstract: We propose a method to construct the initial tensor representation of partition functions and observables for the tensor renormalization group (TRG). The TRG is a numerical calculation technique that utilizes a tensor network representations of physical quantities to investigate physical properties without encountering the sign problem. To apply the TRG, it is essential to construct a locally connected tensor network suitable for recursive coarse-graining. We present a systematic approach for translating a general tensor representation of the partition function to this form. Furthermore, we show the dependence of TRG algorithms on the choice of the initial tensor network representation and propose an improvement of TRG algorithms in this respect

Almost Strong Zero Modes at Finite Temperature

Authors: Niklas Tausendpfund, Aditi Mitra, Matteo Rizzi

arXiv ID: 2501.11121 | Date: 2025-01-19

Abstract: Interacting fermionic chains exhibit extended regions of topological degeneracy of their ground states as a result of the presence of Majorana or parafermionic zero modes localized at the edges. In the opposite limit of infinite temperature, the corresponding non-integrable spin chains, obtained via generalized Jordan-Wigner mapping, are known to host so-called Almost Strong Zero Modes, which are long-lived with respect to any bulk excitations. Here, we study the fairly unexplored territory that bridges these two extreme cases of zero and infinite temperature. We blend two established techniques for states, the Lanczos series expansion and a tensor network ansatz, uplifting them to the level of operator algebra. This allows us to efficiently simulate large system sizes for arbitrarily long timescales and to extract the temperature-dependent decay rates. We observe that for the Kitaev-Hubbard model, the decay rate of the edge mode depends exponentially on the inverse temperature ββ, and on an effective energy scale ΔeffΔ_{\rm eff} that is greater than the thermodynamic gap of the system ΔΔ.

Hamiltonian Lattice Gauge Theories: emergent properties from Tensor Network methods

Authors: Giovanni Cataldi

arXiv ID: 2501.11115 | Date: 2025-01-19

Abstract: This thesis develops advanced Tensor Network (TN) methods to address Hamiltonian Lattice Gauge Theories (LGTs), overcoming limitations in real-time dynamics and finite-density regimes. A novel dressed-site formalism is introduced, enabling efficient truncation of gauge fields while preserving gauge invariance for both Abelian and non-Abelian theories. This formalism is successfully applied to SU(2) Yang-Mills LGTs in two dimensions, providing the first TN simulations of this system and revealing critical aspects of its phase diagram and non-equilibrium behavior, such as a Quantum Many-Body (QMB) scarring dynamics. A generalization of the dressed-site formalism is proposed through a new fermion-to-qubit mapping for general lattice fermion theories, revealing powerful for classical and quantum simulations. Numerical innovations, including the use of optimal space-filling curves such as the Hilbert curve to preserve locality in high-dimensional simulations, further enhance the efficiency of these methods. Together with high-performance computing techniques, these advances open current and future development pathways toward optimized, efficient, and faster simulations on scales comparable to Monte Carlo state-of-the-art.

On the correlation between entanglement and the negative sign problem

Authors: Ping Xu, Yang Shen, Yuan-Yao He, Mingpu Qin

arXiv ID: 2501.11022 | Date: 2025-01-19

Abstract: In this work, we study the correlation between entanglement and the negative sign problem in quantum Monte Carlo for the simulation of low-dimensional strongly correlated quantum many body systems. Entanglement entropy characterizes the difficulty of many-body simulation with tensor network state related methods, while the average sign measures the difficulty in many-body simulation for a variety of quantum Monte Carlo methods. Although there exist cases where one type of method works better than the other, it is desirable to find the possible correlation between entanglement and average sign for general hard strongly correlated systems regarding computational complexity. We take the doped two-dimensional Hubbard model as an example and numerically calculate the doping evolution of both the entanglement in the ground state with Density Matrix Renormalization Group and the average sign in the Auxiliary Field Quantum Monte Carlo simulation at low temperature. The results show that they are indeed correlated. The entanglement entropy (average sign) shows a peak (dip) around 20% doping, indicating that it is the difficult region for both methods. The vicinity of 20% doping is also the most intriguing region in both the Hubbard model and cuprate high-Tc superconductors where competing states with close energy intertwine with each other. Recognizing the correlation between entanglement and average sign provides new insight into our understanding of the difficulty in the simulation of strongly correlated quantum many-body systems.

A Faster Quantum Fourier Transform

Authors: Ronit Shah

arXiv ID: 2501.12414 | Date: 2025-01-19

Abstract: We present an asymptotically improved algorithm for implementing the Quantum Fourier Transform (QFT) in both the exact and approximate settings. Historically, the approximate QFT has been implemented in Θ(nlogn)Θ(n \log n) gates, and the exact in Θ(n2)Θ(n^2) gates. In this work, we show that these costs can be reduced by leveraging a novel formulation of the QFT that recurses on two partitions of the qubits. Specifically, our approach yields an Θ(n(loglogn)2)Θ(n(\log \log n)^2) algorithm for the approximate QFT using Θ(logn)Θ(\log n) ancillas, and an Θ(n(logn)2)Θ(n(\log n)^2) algorithm for the exact QFT requiring Θ(n)Θ(n) ancillas.

Rényi Entanglement of Purification and Half Rényi Reflected Entropy in Free Scalar Theory

Authors: Liangyu Chen

arXiv ID: 2501.10944 | Date: 2025-01-19

Abstract: In the AdS/CFT context, the entanglement of purification (EoP, denoted as EPE_{P}) of CFT is conjectured to be dual to the entanglement wedge cross section (EWCS) in bulk. However, another quantity called reflected entropy SRS_{R} is also supposed to be dual to two times the EWCS. A natural question is whether they are the same in holographic CFTs even though they are different in general. Previous studies have shown EP12SR(n),n2E_{P} \ge \frac{1}{2} S_{R}^{(n)}, n \ge2 for random tensor networks. In this paper, we study this inequality beyond n2n \ge 2, and we focus on the range 0<n<20 < n < 2. However, the calculations of EoP are notoriously difficult in general. Thus, our calculations mainly focus on the free scalar theory which is close to the holographic CFTs. We generalized the previous strategy for EoP in \cite{Takayanagi:2018sbw} to the Rényi case. And we have also presented two methods for Rényi reflected entropy, one is using correlators, the other one is Gaussian wavefunction ansatz. Our calculations show that the inequality still holds for 0<n<20 < n < 2, and it may give us some insights into the equivalence of EoP and half reflected entropy in holographic CFTs. As byproducts of our research, we have also demonstrated the positivity of the Rényi Markov gap and the monotonicity of the Rényi reflected entropy in the free scalar theory.

Unraveling screening mechanisms in Kondo impurities using an NRG-MPS-based method

Authors: Lidia Stocker, Oded Zilberberg

arXiv ID: 2501.10746 | Date: 2025-01-18

Abstract: The Kondo effect is a hallmark of strongly-correlated systems, where an impurity's local degrees of freedom are screened by conduction electrons, forming a many-body singlet. With increasing degrees of freedom in the impurity, theoretical studies face significant challenges in accurately identifying and characterizing the underlying mechanisms that screen the impurity. In this work, we introduce a straightforward yet powerful methodology for identifying the formation of Kondo singlets and their screening mechanisms, by utilizing the numerical renormalization group (NRG) combined with the matrix product states (MPS) technique. We demonstrate the effectiveness of our method on the single and two-level Anderson impurity models (AIM). Furthermore, we discuss potential generalizations of the method to multichannel and multiorbital Kondo impurities. Harnessing advanced tensor network techniques, our approach extends to complex impurity systems, offering a robust and versatile framework for studying Kondo physics.

Parent Lindbladians for Matrix Product Density Operators

Authors: Yuhan Liu, Alberto Ruiz-de-Alarcón, Georgios Styliaris, Xiao-Qi Sun, David Pérez-García, J. Ignacio Cirac

arXiv ID: 2501.10552 | Date: 2025-01-17

Abstract: Understanding quantum phases of matter is a fundamental goal in physics. For pure states, the representatives of phases are the ground states of locally interacting Hamiltonians, which are also renormalization fixed points (RFPs). These RFP states are exactly described by tensor networks. Extending this framework to mixed states, matrix product density operators (MPDOs) which are RFPs are believed to encapsulate mixed-state phases of matter in one dimension, where non-trivial topological phases have already been shown to exist. However, to better motivate the physical relevance of those states, and in particular the physical relevance of the recently found non-trivial phases, it remains an open question whether such MPDO RFPs can be realized as steady states of local Lindbladians. In this work, we resolve this question by analytically constructing parent Lindbladians for MPDO RFPs. These Lindbladians are local, frustration-free, and exhibit minimal steady-state degeneracy. Interestingly, we find that parent Lindbladians possess a rich structure that distinguishes them from their Hamiltonian counterparts. In particular, we uncover an intriguing connection between the non-commutativity of the Lindbladian terms and the fact that the corresponding MPDO RFP belongs to a non-trivial phase.

Cooper-Pair Localization in the Magnetic Dynamics of a Cuprate Ladder

Authors: A. Scheie, P. Laurell, J. Thomas, V. Sharma, A. I. Kolesnikov, G. E. Granroth, Q. Zhang, B. Lake, M. Mihalik, R. I. Bewley, R. S. Eccleston, J. Akimitsu, E. Dagotto, C. D. Batista, G. Alvarez, S. Johnston, D. A. Tennant

arXiv ID: 2501.10296 | Date: 2025-01-17

Abstract: We investigate the spin dynamics of the cuprate ladder Sr2.5_{2.5}Ca11.5_{11.5}Cu24_{24}O41_{41} to elucidate the behavior of its intrinsically doped holes. Combining high-resolution neutron spectroscopy and density matrix renormalization group calculations enables a comprehensive analysis of the collective magnetic dynamics. We find a general absence of magnetic signatures from unpaired charges, indicating holes within the system form strongly bound localized Cooper pairs. A one-band Hubbard model fails to match the spectral features but a straightforward extension to a large attractive nearest-neighbor interaction quantitatively explains our results. Our finding shows the significance of additional interactions beyond the long-predicted quantum spin pairing in the (dd-wave) charge pairing process. Considering the parallels between ladders and two-dimensional cuprates, these results are potentially relevant for square lattices as well.

Beyond-Hubbard pairing in a cuprate ladder

Authors: Hari Padma, Jinu Thomas, Sophia TenHuisen, Wei He, Ziqiang Guan, Jiemin Li, Byungjune Lee, Yu Wang, Seng Huat Lee, Zhiqiang Mao, Hoyoung Jang, Valentina Bisogni, Jonathan Pelliciari, Mark P. M. Dean, Steven Johnston, Matteo Mitrano

arXiv ID: 2501.10287 | Date: 2025-01-17

Abstract: The Hubbard model is believed to capture the essential physics of cuprate superconductors. However, recent theoretical studies suggest that it fails to reproduce a robust and homogeneous superconducting ground state. Here, using resonant inelastic x-ray scattering and density matrix renormalization group calculations, we show that magnetic excitations in the prototypical cuprate ladder Sr14_{14}Cu24_{24}O41_{41} are inconsistent with those of a simple Hubbard model. The magnetic response of hole carriers, contributing to an emergent branch of spin excitations, is strongly suppressed. This effect is the consequence of d-wave-like pairing, enhanced by nearly an order of magnitude through a large nearest-neighbor attractive interaction. The similarity between cuprate ladders and the two-dimensional compounds suggests that such an enhanced hole pairing may be a universal feature of superconducting cuprates.

Exploring Unique Characteristics in Stark Many-Body Localization

Authors: Chung Po Ching

arXiv ID: 2501.10211 | Date: 2025-01-17

Abstract: Stark Many-Body Localization (MBL) is a phenomenon observed in quantum systems in the absence of disorder, where the presence of a linear potential, known as the Stark field, causes the localization. Our study aims to provide novel insight into the properties of Stark MBL and to discover unique entanglement characteristics specific to this phenomenon. The phase diagram analysis reveals different behavior with varying interaction strengths. Furthermore, we highlight the influence of domain wall structures on the breakdown of the entanglement entropy of the system. Moreover, the investigation of Out-of-Time-Ordered Correlator (OTOC) behavior demonstrates distinct responses to interactions based on domain wall configurations. Our findings contribute to a better understanding of Stark MBL and offer valuable insights into the entanglement properties of systems subjected to Stark potentials.

A relativistic continuous matrix product state study of field theories with defects

Authors: Karan Tiwana, Edoardo Lauria, Antoine Tilloy

arXiv ID: 2501.09797 | Date: 2025-01-16

Abstract: We propose a method to compute expectation values in 1+1-dimensional massive Quantum Field Theories (QFTs) with line defects using Relativistic Continuous Matrix Product State (RCMPS). Exploiting Euclidean invariance, we use a quantization scheme where (imaginary) time runs perpendicularly to the defect. With this choice, correlation functions of local operators in the presence of the defect can be computed as expectation values of extended operators in the no-defect vacuum, which can be approximated by a homogeneous RCMPS. We demonstrate the effectiveness of this machinery by computing correlation functions of local bulk and defect operators in φ4φ^4 theory with a magnetic line defect, in perturbative, strong coupling, critical, and symmetry-broken regimes.

Riemannian quantum circuit optimization based on matrix product operators

Authors: Isabel Nha Minh Le, Shuo Sun, Christian B. Mendl

arXiv ID: 2501.08872 | Date: 2025-01-15

Abstract: We significantly enhance the simulation accuracy of initial Trotter circuits for Hamiltonian simulation of quantum systems by integrating first-order Riemannian optimization with tensor network methods. Unlike previous approaches, our method imposes no symmetry assumptions, such as translational invariance, on the quantum systems. This technique is scalable to large systems through the use of a matrix product operator representation of the reference time evolution propagator. Our optimization routine is applied to various spin chains and fermionic systems described by the transverse-field Ising Hamiltonian, the Heisenberg Hamiltonian, and the spinful Fermi-Hubbard Hamiltonian. In these cases, our approach achieves a relative error improvement of up to four orders of magnitude for systems of 50 qubits, although our method is also applicable to larger systems. Furthermore, we demonstrate the versatility of our method by applying it to molecular systems, specifically lithium hydride, achieving an error improvement of up to eight orders of magnitude. This proof of concept highlights the potential of our approach for broader applications in quantum simulations.

Breakdown of superdiffusion in perturbed quantum integrable spin chains and ladders

Authors: Kevin Wang, Joel E. Moore

arXiv ID: 2501.08866 | Date: 2025-01-15

Abstract: Superdiffusive transport with dynamical exponent z=3/2z=3/2 has been firmly established at finite temperature for a class of integrable systems with a non-abelian global symmetry GG. On the inclusion of integrability-breaking perturbations, diffusive transport with z=2z=2 is generically expected to hold in the limit of late time. Recent studies of the classical Haldane-Ishimori-Skylanin model have found that perturbations that preserve the global symmetry lead to a much slower timescale for the onset of diffusion, albeit with uncertainty over the exact scaling exponent. That is, for perturbations of strength λλ, the characteristic timescale for diffusion goes as tλαt_*\sim λ^{-α} for some αα. Using large-scale matrix product state simulations, we investigate this behavior for perturbations to the canonical quantum model showing superdiffusion: the S=1/2S=1/2 quantum Heisenberg chain. We consider a ladder configuration and look at various perturbations that either break or preserve the SU(2)SU(2) symmetry, leading to scaling exponents consistent with those observed in one classical study arXiv:2402.18661: α=2α=2 for symmetry-breaking terms and α=6α=6 for symmetry-preserving terms. We also consider perturbations from another integrable point of the ladder model with G=SU(4)G=SU(4) and find consistent results. Finally, we consider a generalization to an SU(3)SU(3) ladder and find that the α=6α=6 scaling appears to be universal across superdiffusive systems when the perturbations preserve the non-abelian symmetry GG.

Quantum disorder induced by nuclear tunneling in lattice

Authors: Yu-Cheng Zhu, Jia-Xi Zeng, Qi-Jun Ye, Xin-Zheng Li

arXiv ID: 2501.08801 | Date: 2025-01-15

Abstract: Lattice degrees of freedom (DoFs) may induce quantum disorder (QD) when nuclear tunneling outvies long-range order, but conventional phonon theory is incapable of describing such QD phases. Here we develop a method based on path-integral molecular dynamics to solve this problem. Its accuracy is verified in a double-well chain model and it is applied to a real material from first principles. A quantum order-disorder-order phase transition sequence is demonstrated when varying the strength of quantum fluctuations using the lattice constants as the tuning factor. Combining the excitation spectra and Rényi entanglement entropy, we pinpoint the QD region. This picture may be general in lattice systems having soft phonon modes, not limited to quantum paraelectricity, in which novel entangled lattice motion and its coupling with other DoFs can be expected.

Transformed Low-rank Adaptation via Tensor Decomposition and Its Applications to Text-to-image Models

Authors: Zerui Tao, Yuhta Takida, Naoki Murata, Qibin Zhao, Yuki Mitsufuji

arXiv ID: 2501.08727 | Date: 2025-01-15

Abstract: Parameter-Efficient Fine-Tuning (PEFT) of text-to-image models has become an increasingly popular technique with many applications. Among the various PEFT methods, Low-Rank Adaptation (LoRA) and its variants have gained significant attention due to their effectiveness, enabling users to fine-tune models with limited computational resources. However, the approximation gap between the low-rank assumption and desired fine-tuning weights prevents the simultaneous acquisition of ultra-parameter-efficiency and better performance. To reduce this gap and further improve the power of LoRA, we propose a new PEFT method that combines two classes of adaptations, namely, transform and residual adaptations. In specific, we first apply a full-rank and dense transform to the pre-trained weight. This learnable transform is expected to align the pre-trained weight as closely as possible to the desired weight, thereby reducing the rank of the residual weight. Then, the residual part can be effectively approximated by more compact and parameter-efficient structures, with a smaller approximation error. To achieve ultra-parameter-efficiency in practice, we design highly flexible and effective tensor decompositions for both the transform and residual adaptations. Additionally, popular PEFT methods such as DoRA can be summarized under this transform plus residual adaptation scheme. Experiments are conducted on fine-tuning Stable Diffusion models in subject-driven and controllable generation. The results manifest that our method can achieve better performances and parameter efficiency compared to LoRA and several baselines.

Superdiffusive transport in chaotic quantum systems with nodal interactions

Authors: Yu-Peng Wang, Jie Ren, Sarang Gopalakrishnan, Romain Vasseur

arXiv ID: 2501.08381 | Date: 2025-01-14

Abstract: We introduce a class of interacting fermionic quantum models in dd dimensions with nodal interactions that exhibit superdiffusive transport. We establish non-perturbatively that the nodal structure of the interactions gives rise to long-lived quasiparticle excitations that result in a diverging diffusion constant, even though the system is fully chaotic. Using a Boltzmann equation approach, we find that the charge mode acquires an anomalous dispersion relation at long wavelength ω(q)qzω(q) \sim q^{z} with dynamical exponent z=min[(2n+d)/2n,2]z={\rm min}[(2n+d)/2n,2], where nn is the order of the nodal point in momentum space. We verify our predictions in one dimensional systems using tensor-network techniques.

Low-temperature Gibbs states with tensor networks

Authors: Denise Cocchiarella, Mari Carmen Bañuls

arXiv ID: 2501.08300 | Date: 2025-01-14

Abstract: We introduce a tensor network method for approximating thermal equilibrium states of quantum many-body systems at low temperatures. Whereas the usual approach starts from infinite temperature and evolves the state in imaginary time (toward lower temperature), our ansatz is constructed from the zero-temperature limit, the ground state, which can be found with a standard tensor network approach. Motivated by properties of the ground state for conformal field theories, our ansatz is especially well suited near criticality. Moreover, it allows an efficient computation of thermodynamic quantities and entanglement properties. We demonstrate the performance of our approach with a tree tensor network ansatz, although it can be extended to other tensor networks, and present results illustrating its effectiveness in capturing the finite-temperature properties in one- and two-dimensional scenarios. In particular, in the critical one-dimensional case we show how the ansatz reproduces the finite temperature scaling of entanglement in a conformal field theory.

Tomonaga-Luttinger Liquid Behavior in a Rydberg-encoded Spin Chain

Authors: Gabriel Emperauger, Mu Qiao, Cheng Chen, Filippo Caleca, Saverio Bocini, Marcus Bintz, Guillaume Bornet, Romain Martin, Bastien Gély, Lukas Klein, Daniel Barredo, Shubhayu Chatterjee, Norman Yao, Fabio Mezzacapo, Thierry Lahaye, Tommaso Roscilde, Antoine Browaeys

arXiv ID: 2501.08179 | Date: 2025-01-14

Abstract: Quantum fluctuations can disrupt long-range order in one-dimensional systems, and replace it with the universal paradigm of the Tomonaga-Luttinger liquid (TLL), a critical phase of matter characterized by power-law decaying correlations and linearly dispersing excitations. Using a Rydberg quantum simulator, we study how TLL physics manifests in the low-energy properties of a spin chain, interacting under either the ferromagnetic or the antiferromagnetic dipolar XY Hamiltonian. Following quasi-adiabatic preparation, we directly observe the power-law decay of spin-spin correlations in real-space, allowing us to extract the Luttinger parameter. In the presence of an impurity, the chain exhibits tunable Friedel oscillations of the local magnetization. Moreover, by utilizing a quantum quench, we directly probe the propagation of correlations, which exhibit a light-cone structure related to the linear sound mode of the underlying TLL. Our measurements demonstrate the influence of the long-range dipolar interactions, renormalizing the parameters of TLL with respect to the case of nearest-neighbor interactions. Finally, comparison to numerical simulations exposes the high sensitivity of TLLs to doping and finite-size effects.

Intricately Entangled Spin and Charge Diffusion and the Coherence-Incoherence Crossover in the High-Dimensional Hubbard Model

Authors: Gopal Prakash, S. R. Hassan, M. S. Laad, N. S. Vidhyadhiraja, T. V. Ramakrishnan

arXiv ID: 2501.08121 | Date: 2025-01-14

Abstract: Correlation-driven metal-insulator transitions and temperature-driven quantum-coherent-to-incoherent crossovers in correlated electron systems underpin the doping, temperature and frequency-resolved evolution of physical responses. Motivated by recent experimental studies that investigate the evolution of dynamical spin and charge responses, we analyze the spin and charge diffusion spectra in both half-filled and doped one-band Hubbard model using Dynamical Mean Field Theory (DMFT) combined with the Numerical Renormalization Group (NRG). We compare the relative strengths and limitations of Density Matrix NRG (DMNRG) and Full Density Matrix NRG (FDM-NRG) in capturing low-frequency spectral features and their evolution with temperature, interaction strength and band-filling. Key measures, including characteristic frequency scales, Kullback-Leibler divergence, diffusion constants, and kurtosis provide complementary but internally consistent picture for the evolution of spin and charge excitations across bandwidth as well as the band-filling driven Mott transitions and the coherent-incoherent crossover. We find that spin and charge fluctuations cross over from quantum-coherent-to-quantum-incoherent at distinct temperatures, providing a microscopic insight into the complex, two-stage, Fermi-to-non-Fermi liquid-to-bad metal crossovers seen in transport data, in particular in the dcdc resistivity.

Effective algorithms for tensor train decomposition via the UTV framework

Authors: Yuchao Wang, Maolin Che, Yimin Wei

arXiv ID: 2501.07904 | Date: 2025-01-14

Abstract: The tensor-train (TT) decomposition is widely used to compress large tensors into a more compact form by exploiting their inherent data structures. A fundamental approach for constructing the TT format is the well-known TT-SVD method, which performs singular value decompositions (SVDs) on the successive matrices sequentially. But in practical applications, it is often unnecessary to compute full SVDs. In this article, we propose a new method called the TT-UTV. It utilizes the virtues of rank-revealing UTV decomposition to compute the TT format for a large-scale tensor, resulting in lower computational cost. We analyze the error bounds on the accuracy of these algorithms in both the URV and ULV cases and then recommend different sweep patterns for these two cases. Based on the theoretical analysis, we also formulate the rank-adaptive algorithms with prescribed accuracy. Numerical experiments on various applications, including magnetic resonance imaging data completion, are performed to illustrate their good performance in practice.

A Low-Rank QTT-based Finite Element Method for Elasticity Problems

Authors: Elena Benvenuti, Gianmarco Manzini, Marco Nale, Simone Pizzolato

arXiv ID: 2501.07778 | Date: 2025-01-14

Abstract: We present an efficient and robust numerical algorithm for solving the two-dimensional linear elasticity problem that combines the Quantized Tensor Train format and a domain partitioning strategy. This approach makes it possible to solve the linear elasticity problem on a computational domain that is more general than a square. Our method substantially decreases memory usage and achieves a notable reduction in rank compared to established Finite Element implementations like the FEniCS platform. This performance gain, however, requires a fundamental rethinking of how core finite element operations are implemented, which includes changes to mesh discretization, node and degree of freedom ordering, stiffness matrix and internal nodal force assembly, and the execution of algebraic matrix-vector operations. In this work, we discuss all these aspects in detail and assess the method's performance in the numerical approximation of three representative test cases.

TeNeS-v2: Enhancement for Real-Time and Finite Temperature Simulations of Quantum Many-Body Systems

Authors: Yuichi Motoyama, Tsuyoshi Okubo, Kazuyoshi Yoshimi, Satoshi Morita, Tatsumi Aoyama, Takeo Kato, Naoki Kawashima

arXiv ID: 2501.07777 | Date: 2025-01-14

Abstract: Quantum many-body systems are challenging targets for computational physics due to their large degrees of freedom. The tensor networks, particularly Tensor Product States (TPS) and Projected Entangled Pair States (PEPS), effectively represent these systems on two-dimensional lattices. However, the technical complexity of TPS/PEPS-based coding is often too much for researchers to handle. To reduce this problem, we developed TeNeS (Tensor Network Solver). This paper introduces TeNeS-v2, which extends TeNeS with real-time and finite temperature simulations, providing deeper insights into quantum many-body systems. We detail the new algorithms, input/output design, and application examples, demonstrating TeNeS-v2's applicability to various quantum spin and Bose models on two-dimensional lattices.

Magnetic phases of the periodic Anderson model in two dimensions

Authors: Imre Hagymási

arXiv ID: 2501.07541 | Date: 2025-01-13

Abstract: We investigate the ground-state properties of the periodic Anderson model on the square lattice across various band fillings. Employing the infinite projected entangled-pair states (iPEPS) technique, we can determine the magnetic ground states accurately and compare them to mean-field predictions to highlight the effects of quantum fluctuations. At half-filling, we analyze the transition between the antiferromagnetic and paramagnetic (Kondo singlet) phases as a function of hybridization and ff-level energy, finding excellent agreement with existing quantum Monte Carlo studies in the case of hybridization. For n=1.5n = 1.5 electrons per site, we identify a novel correlated antiferromagnetic diagonal stripe phase as the ground state, which competes with its ferromagnetic partner state.

Provable Low-Rank Tensor-Train Approximations in the Inverse of Large-Scale Structured Matrices

Authors: Chuanfu Xiao, Kejun Tang, Zhitao Zhu

arXiv ID: 2501.07210 | Date: 2025-01-13

Abstract: This paper studies the low-rank property of the inverse of a class of large-scale structured matrices in the tensor-train (TT) format, which is typically discretized from differential operators. An interesting question that we are concerned with is: Does the inverse of the large-scale structured matrix still admit the low-rank TT representation with guaranteed accuracy? In this paper, we provide a computationally verifiable sufficient condition such that the inverse matrix can be well approximated in a low-rank TT format. It not only answers what kind of structured matrix whose inverse has the low-rank TT representation but also motivates us to develop an efficient TT-based method to compute the inverse matrix. Furthermore, we prove that the inverse matrix indeed has the low-rank tensor format for a class of large-scale structured matrices induced by differential operators involved in several PDEs, such as the Poisson, Boltzmann, and Fokker-Planck equations. Thus, the proposed algorithm is suitable for solving these PDEs with massive degrees of freedom. Numerical results on the Poisson, Boltzmann, and Fokker-Planck equations validate the correctness of our theory and the advantages of our methodology.

Tensorization of neural networks for improved privacy and interpretability

Authors: José Ramón Pareja Monturiol, Alejandro Pozas-Kerstjens, David Pérez-García

arXiv ID: 2501.06300 | Date: 2025-01-10

Abstract: We present a tensorization algorithm for constructing tensor train representations of functions, drawing on sketching and cross interpolation ideas. The method only requires black-box access to the target function and a small set of sample points defining the domain of interest. Thus, it is particularly well-suited for machine learning models, where the domain of interest is naturally defined by the training dataset. We show that this approach can be used to enhance the privacy and interpretability of neural network models. Specifically, we apply our decomposition to (i) obfuscate neural networks whose parameters encode patterns tied to the training data distribution, and (ii) estimate topological phases of matter that are easily accessible from the tensor train representation. Additionally, we show that this tensorization can serve as an efficient initialization method for optimizing tensor trains in general settings, and that, for model compression, our algorithm achieves a superior trade-off between memory and time complexity compared to conventional tensorization methods of neural networks.

Diabatic error and propagation of Majorana zero modes in interacting quantum dots systems

Authors: Bradraj Pandey, Gaurav Kumar Gupta, Gonzalo Alvarez, Satoshi Okamoto, Elbio Dagotto

arXiv ID: 2501.06288 | Date: 2025-01-10

Abstract: Motivated by recent experimental progress in realizing Majorana zero modes (MZMs) using quantum dot systems, we investigate the diabatic errors associated with the movement of those MZMs. The movement is achieved by tuning time-dependent gate potentials applied to individual quantum dots, effectively creating a moving potential wall. To probe the optimized movement of MZMs, we calculate the experimentally accessible local density-of-states and time-dependent fidelity using many-body time-dependent numerical methods. Our analysis reveals that an optimal potential wall height is crucial to preserve the well-localized nature of the MZM during its movement. Moreover, for the first time, we analyze diabatic errors in realistic quantum-dot systems, incorporating the effects of repulsive Coulomb interactions and disorder in both hopping and pairing terms. Additionally, we provide a comparative study of diabatic errors arising from the simultaneous versus sequential tuning of multiple gates during the MZMs movement. Finally, we estimate the time scale required for MZM transfer in a six-quantum-dot system, demonstrating that MZM movement is feasible and can be completed well within the qubit's operational lifetime in practical quantum-dot setups.

The weak equivalence principle and the Dirac constant: A result from the holographic principle

Authors: Eiji Konishi

arXiv ID: 2501.07594 | Date: 2025-01-09

Abstract: In this article, based on a recent formularization of the holographic principle proposed and investigated by the present author, we show that the weak equivalence principle in general relativity is equivalent to the equivalence between two forms of the Dirac constant, that is, the action of the spin degree of freedom in the two-dimensional Hilbert space and the lower bound in the quantum mechanical uncertainty relations. This result follows from an equation between the Euclidean and Lorentzian world-line actions of a massive particle divided by the Dirac constant, via the Wick rotation, by using the Euclidean and Lorentzian actions of a holographic tensor network, whose quantum state is classicalized by introducing the superselection rule.

Kondo impurity in an attractive Fermi-Hubbard bath: Equilibrium and dynamics

Authors: Zhi-Yuan Wei, Tao Shi, J. Ignacio Cirac, Eugene A. Demler

arXiv ID: 2501.05562 | Date: 2025-01-09

Abstract: We investigate theoretically equilibrium and dynamical properties of a Kondo impurity coupled to either 1D or 2D superconductors, modeled by the attractive Fermi-Hubbard model. By employing a non-Gaussian variational approach, we go beyond the approximation of a constant superconducting (SC) gap. We show that dynamical properties of the system can be modified qualitatively, when space and time dependent renormalization of the SC gap and electron-impurity hybridization are included. For the ground state, we find the singlet-doublet phase transition and ππ-phase shifts of the SC order parameter. For dynamics, first we consider spin dynamics following an abrupt connection of the polarized impurity to the 2D bath. We find rapid relaxation of impurity polarization and directional emission of a magnetization pulse, which becomes damped as it propagates into the bulk. Then we analyze transport between two SC leads coupled through the impurity at finite bias voltage. Here we go beyond analysis of the steady state to investigate full-time dynamics following an abrupt application of the bias voltage. We uncover four distinct regimes in the transient dynamics and transport properties: (I) the AC Josephson effect regime; (II) dynamical competition between charge-density-wave (CDW) and SC orders with transient Kondo correlations; (III) the coexistence of AC and DC currents facilitated by partial Kondo screening and dynamical stabilization of the SC order; (IV) DC Kondo transport regime modified by the SC order. Regime II exhibits a dynamical transition from SC to CDW order that locally restores the U(1) symmetry. We argue that our findings for regime IV provide a theoretical explanation for the experimentally observed anomalous enhancement of DC conductance and suppression of the AC Josephson current. Finally, we discuss the potential experimental realization with ultracold atoms.

Fermionic cellular automata in one dimension

Authors: Lorenzo S. Trezzini, Matteo Lugli, Paolo Meda, Alessandro Bisio, Paolo Perinotti, Alessandro Tosini

arXiv ID: 2501.05349 | Date: 2025-01-09

Abstract: We consider quantum cellular automata for one-dimensional chains of Fermionic modes and study their implementability as finite depth quantum circuits. Fermionic automata have been classified in terms of an index modulo circuits and the addition of ancillary systems. We strengthen this result removing the ancilla degrees of freedom in defining the equivalence classes. A complete characterization of nearest-neighbours automata is given. A class of Fermionic automata is found which cannot be expressed in terms of single mode and controlled-phase gates composed with shifts, as is the case for qubit cellular automata.

The application of annealing in quantum cooling protocols

Authors: Chongyuan Xu

arXiv ID: 2501.05268 | Date: 2025-01-09

Abstract: Inspired by simulated annealing algorithm, we propose a quantum cooling protocol which includes an annealing process. This protocol can be universally and efficiently applied to various quantum simulators, driving the system from an arbitrary initial state to the ground state with high fidelity. We have described the cooling process based on perturbation theory, validated the advantages of bath under time-modulated Zeeman field compared to bath under static one, and provided a justification for the necessity of an annealing process when the system to be cooled is unknown. We applied tensor network methods to numerically simulate our cooling protocol, using the transverse field Ising model (TFIM) as an example to verify the effectiveness of the protocol in cooling one-dimensional systems, two-dimensional systems, and systems with quantum noise. We compared the overall performance of cooling protocols with and without the annealing process on a test set generated with random parameters gPg_P. The results indicate that the cooling protocol with annealing process can achieve both accuracy and efficiency. Our results also show that the cooling protocol's resistance to noise depends on the type of quantum noise.

Research on quantum compilation of neutral atom quantum computing platform

Authors: Chongyuan Xu

arXiv ID: 2501.05266 | Date: 2025-01-09

Abstract: Quantum compilation is the process of decomposing high-level quantum algorithms or arbitrary unitary operations into quantum circuits composed of a specific set of quantum gates. Neutral atom quantum computing platform is a quantum computing implementation method with high controllability and scalability, but its quantum compilation method is not mature. We systematically review the quantum compilation methods based on matrix decomposition, and propose a compilation algorithm suitable for neutral atom quantum computing, which can effectively decompose any unitary operation into a series of quantum gates suitable for the neutral atom platform, and ensure that the generated quantum circuits can run directly on the platform.

Low-Rank Reduced Biquaternion Tensor Ring Decomposition and Tensor Completion

Authors: Hui Luo, Xin Liu, Wei Liu, Yang Zhang

arXiv ID: 2501.04948 | Date: 2025-01-09

Abstract: We define the reduced biquaternion tensor ring (RBTR) decomposition and provide a detailed exposition of the corresponding algorithm RBTR-SVD. Leveraging RBTR decomposition, we propose a novel low-rank tensor completion algorithm RBTR-TV integrating RBTR ranks with total variation (TV) regularization to optimize the process. Numerical experiments on color image and video completion tasks indicate the advantages of our method.

Non-Markovian dynamics of generation of bound states in the continuum via single-photon scattering

Authors: Giuseppe Magnifico, Maria Maffei, Domenico Pomarico, Debmalya Das, Paolo Facchi, Saverio Pascazio, Francesco V. Pepe

arXiv ID: 2501.04691 | Date: 2025-01-08

Abstract: The excitation of bound states in the continuum (BICs) in two- or multi-qubit systems lies at the heart of entanglement generation and harnessing in Waveguide Quantum Electrodynamics platforms. However, the generation of qubit pair BICs through single-photon scattering is hindered by the fact that these states are effectively decoupled from propagating photons. We prove that scattering of a parity-invariant single photon on a qubit pair, combined with a properly engineered time variation of the qubit detuning, is not only feasible, but also more effective than strategies based on the relaxation of the excited states of the qubits when the distance between the qubits gives rise to non-negligible photon delays (non-Markovian regime). The use of tensor network methods to simulate the proposed scheme enables to include such photon delays in collision models, thus opening the possibility to follow the time evolution of the full quantum system, including qubits and field, and to efficiently implement and characterize the dynamics hence identifying optimal working points for the BIC generation.

Exploring nontrivial topology at quantum criticality in a superconducting processor

Authors: Ziqi Tan, Ke Wang, Sheng Yang, Fanhao Shen, Feitong Jin, Xuhao Zhu, Yujie Ji, Shibo Xu, Jiachen Chen, Yaozu Wu, Chuanyu Zhang, Yu Gao, Ning Wang, Yiren Zou, Aosai Zhang, Tingting Li, Zehang Bao, Zitian Zhu, Jiarun Zhong, Zhengyi Cui, Yihang Han, Yiyang He, Han Wang, Jianan Yang, Yanzhe Wang, Jiayuan Shen, Gongyu Liu, Zixuan Song, Jinfeng Deng, Hang Dong, Pengfei Zhang, Shao-Kai Jian, Hekang Li, Zhen Wang, Qiujiang Guo, Chao Song, Xue-Jia Yu, H. Wang, Hai-Qing Lin, Fei Wu

arXiv ID: 2501.04679 | Date: 2025-01-08

Abstract: The discovery of nontrivial topology in quantum critical states has introduced a new paradigm for classifying quantum phase transitions and challenges the conventional belief that topological phases are typically associated with a bulk energy gap. However, realizing and characterizing such topologically nontrivial quantum critical states with large particle numbers remains an outstanding experimental challenge in statistical and condensed matter physics. Programmable quantum processors can directly prepare and manipulate exotic quantum many-body states, offering a powerful path for exploring the physics behind these states. Here, we present an experimental exploration of the critical cluster Ising model by preparing its low-lying critical states on a superconducting processor with up to 100100 qubits. We develop an efficient method to probe the boundary gg-function based on prepared low-energy states, which allows us to uniquely identify the nontrivial topology of the critical systems under study. Furthermore, by adapting the entanglement Hamiltonian tomography technique, we recognize two-fold topological degeneracy in the entanglement spectrum under periodic boundary condition, experimentally verifying the universal bulk-boundary correspondence in topological critical systems. Our results demonstrate the low-lying critical states as useful quantum resources for investigating the interplay between topology and quantum criticality.

Incommensurate quantum magnet based on 4f-electron in a zigzag spin-1/2 chain of YbCuS2_2

Authors: T. Onimaru, Y. Ohmagari, S. Mizutani, R. Yamamoto, H. Kaneshima, C. Moriyoshi, D. T. Adroja, D. Khyalyavin, P. Manuel, H. Saito, C. Hotta

arXiv ID: 2501.04533 | Date: 2025-01-08

Abstract: We performed high-resolution powder neutron diffraction experiments and discovered an elliptic helical incommensurate magnetic structure in the semiconducting rare-earth magnet YbCuS2, featuring effective spin-1/2 Yb3+^{3+} ions that form a zigzag chain. Upon cooling the sample to 0.2 K, we observed very weak magnetic peaks indexed with an incommensurate propagation vector k = [0, 0.305, 0] along the zigzag chain. The magnitude of the magnetic moment is at least one-third smaller than the expected value for the Yb3+^{3+} Kramers doublet ground state. In an applied magnetic field, up-up-down magnetic order was observed at 7.5 T, characterized by diffraction peaks indexed with k = [0, 1/3, 0] and substantial uniform magnetic components. These observations agree well with theoretical calculations based on the density matrix renormalization group for a zigzag spin-1/2 model with isotropic Heisenberg interactions and off-diagonal symmetric ΓΓ-type exchange interactions derived from material parameters. The theory elucidates the quantum mechanical nature of the incommensurate magnetism as remnant off-diagonal spin correlations in a nematic dimer-singlet state.

Automatic partitioning for the low-rank integration of stochastic Boolean reaction networks

Authors: Lukas Einkemmer, Julian Mangott, Martina Prugger

arXiv ID: 2501.04157 | Date: 2025-01-07

Abstract: Boolean reaction networks are an important tool in biochemistry for studying mechanisms in the biological cell. However, the stochastic formulation of such networks requires the solution of a master equation which inherently suffers from the curse of dimensionality. In the past, the dynamical low-rank (DLR) approximation has been repeatedly used to solve high-dimensional reaction networks by separating the network into smaller partitions. However, the partitioning of these networks was so far only done by hand. In this paper, we present a heuristic, automatic partitioning scheme based on two ingredients: the Kernighan-Lin algorithm and information entropy. Our approach is computationally inexpensive and can be easily incorporated as a preprocessing step into the existing simulation workflow. We test our scheme by partitioning Boolean reaction networks on a single level and also in a hierarchical fashion with tree tensor networks. The resulting accuracy of the scheme is superior to both partitionings chosen by human experts and those found by simply minimizing the number of reaction pathways between partitions.

Field-Induced Ordered Phases in Anisotropic Spin-1/2 Kitaev Chains

Authors: Mandev Bhullar, Haoting Xu, Hae-Young Kee

arXiv ID: 2501.03329 | Date: 2025-01-06

Abstract: Motivated by intense research on two-dimensional spin-1/2 Kitaev materials, Kitaev spin chains and ladders, though geometrically limited, have been studied for their numerical simplicity and insights into extended Kitaev models. The phase diagrams under the magnetic field were also explored for these quasi-one dimensional models. For an isotropic Kitaev chain, it was found that a magnetic field polarizes the ground state except along the symmetric field angle, where the chain is found to remain gapless up to a critical field strength where it enters an intriguing soliton phase before reaching the polarized state at higher field strengths. Here we study an anisotropic Kitaev chain under a magnetic field using the density matrix renormalization group technique, where the ground state has a macroscopic degeneracy with a finite gap in the absence of the magnetic field. When the field is mainly aligned parallel to the strong bond, four-site and large unit-cell ordered phases arise. In a certain angle of the field, another ordered phase characterized by a uniform chirality with six-site periodicity emerges. We employ a perturbation theory to understand such field-induced ordered phases. The effective model uncovers the presence of transverse Ising and Dzyaloshinskii-Moriya interactions between unit cells, as well as further-neighbor Ising interaction induced by the magnetic field, which collectively explain the mechanisms behind these ordered states. Open questions and challenges are also discussed.

Enhancing Quantum State Reconstruction with Structured Classical Shadows

Authors: Zhen Qin, Joseph M. Lukens, Brian T. Kirby, Zhihui Zhu

arXiv ID: 2501.03144 | Date: 2025-01-06

Abstract: Quantum state tomography (QST) remains the prevailing method for benchmarking and verifying quantum devices; however, its application to large quantum systems is rendered impractical due to the exponential growth in both the required number of total state copies and classical computational resources. Recently, the classical shadow (CS) method has been introduced as a more computationally efficient alternative, capable of accurately predicting key quantum state properties. Despite its advantages, a critical question remains as to whether the CS method can be extended to perform QST with guaranteed performance. In this paper, we address this challenge by introducing a projected classical shadow (PCS) method with guaranteed performance for QST based on Haar-random projective measurements. PCS extends the standard CS method by incorporating a projection step onto the target subspace. For a general quantum state consisting of nn qubits, our method requires a minimum of O(4n)O(4^n) total state copies to achieve a bounded recovery error in the Frobenius norm between the reconstructed and true density matrices, reducing to O(2nr)O(2^n r) for states of rank r<2nr<2^n -- meeting information-theoretic optimal bounds in both cases. For matrix product operator states, we demonstrate that the PCS method can recover the ground-truth state with O(n2)O(n^2) total state copies, improving upon the previously established Haar-random bound of O(n3)O(n^3). Simulation results further validate the effectiveness of the proposed PCS method.

Stable excitations and holographic transportation in tensor networks of critical spin chains

Authors: Zuo Wang, Liang He

arXiv ID: 2501.03084 | Date: 2025-01-06

Abstract: The AdS/CFT correspondence conjectures a duality between quantum gravity theories in anti-de Sitter (AdS) spacetime and conformal field theories (CFTs) on the boundary. One intriguing aspect of this correspondence is that it offers a pathway to explore quantum gravity through tabletop experiments. Recently, a multi-scale entanglement renormalization ansatz (MERA) model of AdS/CFT that can be implemented using contemporary quantum simulators has been proposed [R. Sahay, M. D. Lukin, and J. Cotler, arXiv:2401.13595 (2024)]. Particularly, local bulk excitations (entitled "hologrons") manifesting attractive interactions given by AdS gravity were found. However, the fundamental question concerning the stability of these identified hologrons is still left open. Here, we address this question and find that hologrons are unstable during dynamic evolution. In searching for stable bulk excitations with attractive interactions, we find they can be constructed by the local primary operators in the boundary CFT. Furthermore, we identify a class of boundary excitations that exhibit the bizarre behavior of "holographic transportation", which can be directly observed on the boundary system implemented in experiments.

Responses for one-dimensional quantum spin systems via tensor networks

Authors: Jiayin Gu

arXiv ID: 2501.01920 | Date: 2025-01-03

Abstract: Tensor networks are adopted to calculate the responses for one-dimensional quantum spin systems that are initially in thermal equilibrium. The Ising chain in mixed transverse and longitudinal fields is used as the benchmarking system. The linear and second-order responses of the magnetization in zz-direction induced by the time-dependent force conjugated with the magnetization in xx-direction are calculated. In addition, the magnetization in zz-direction is also exactly calculated in response to this excitation. As expected, the first two responses are shown to be excellent corrections to the equilibrium magnetization in zz-direction when the excitation is weak. This result represents an illustrative example of the response theory for nontrivial quantum many-body systems.

Noise-Mitigated Variational Quantum Eigensolver with Pre-training and Zero-Noise Extrapolation

Authors: Wanqi Sun, Jungang Xu, Chenghua Duan

arXiv ID: 2501.01646 | Date: 2025-01-03

Abstract: As a hybrid quantum-classical algorithm, the variational quantum eigensolver is widely applied in quantum chemistry simulations, especially in computing the electronic structure of complex molecular systems. However, on existing noisy intermediate-scale quantum devices, some factors such as quantum decoherence, measurement errors, and gate operation imprecisions are unavoidable. To overcome these challenges, this study proposes an efficient noise-mitigating variational quantum eigensolver for accurate computation of molecular ground state energies in noisy environments. We design the quantum circuit with reference to the structure of matrix product states and utilize it to pre-train the circuit parameters, which ensures circuit stability and mitigates fluctuations caused by initialization. We also employ zero-noise extrapolation to mitigate quantum noise and combine it with neural networks to improve the accuracy of the noise-fitting function, which significantly eliminates noise interference. Furthermore, we implement an intelligent grouping strategy for measuring Hamiltonian Pauli strings, which not only reduces measurement errors but also improves sampling efficiency. We perform numerical simulations to solve the ground state energy of the H4H_4 molecule by using MindSpore Quantum framework, and the results demonstrate that our algorithm can constrain noise errors within the range of O(102)O(101)\mathcal{O}(10^{-2}) \sim \mathcal{O}(10^{-1}), outperforming mainstream variational quantum eigensolvers. This work provides a new strategy for high-precision quantum chemistry calculations on near-term noisy quantum hardware. The updated code is available at https://gitee.com/mindspore/mindquantum/tree/research/paper_with_code/eigensolver_with_mps_and_ZNE or https://github.com/mindspore-lab/models/tree/master/research/arxiv_papers/MPS_eigensolver_with_ZNE.

Tensor network method for solving the Ising model with a magnetic field

Authors: Myung-Hoon Chung

arXiv ID: 2501.01098 | Date: 2025-01-02

Abstract: We study the two-dimensional square lattice Ising ferromagnet and antiferromagnet with a magnetic field by using tensor network method. Focusing on the role of guage fixing, we present the partition function in terms of a tensor network. The tensor has a different symmetry property for ferromagnets and antiferromagnets. The tensor network of the partition function is interpreted as a multiple product of the one-dimensional quantum Hamiltonian. We perform infinite density matrix renormalization group to contract the two-dimensional tensor network. We present the numerical result of magnetization and entanglement entropy for the Ising ferromagnet and antiferromagnet side by side. In order to determine the critical line in the parameter space of temperature and magnetic field, we use the half-chain entanglement entropy of the one-dimensional quantum state. The entanglement entropy precisely indicates the critical line forming the parabolic shape for the antiferromagnetic case, but shows the critical point for the ferromagnetic case.

Quantum many-body dynamics for fermionic t-J model simulated with atom arrays

Authors: Ye-Bing Zhang, Xin-Chi Zhou, Bao-Zong Wang, Xiong-Jun Liu

arXiv ID: 2501.00552 | Date: 2024-12-31

Abstract: The fermionic t-J model has been widely recognized as a canonical model for broad range of strongly correlated phases, particularly the high-Tc superconductor. Simulating this model with controllable quantum platforms offers new possibilities to probe high-Tc physics, yet suffering challenges. Here we propose a novel scheme to realize a highly-tunable extended t-J model in a programmable Rydberg-dressed tweezer array. Through engineering the Rydberg-dressed dipole-dipole interaction and inter-tweezer couplings, the fermionic t-J model with independently tunable exchange and hopping couplings is achieved. With the high tunability, we explore quantum many-body dynamics in the large J/t limit, a regime well beyond the conventional optical lattices and cuprates, and predict an unprecedented many-body self-pinning effect enforced by local quantum entanglement with emergent conserved quantities. The self-pinning effect leads to novel nonthermal quantum many-body dynamics, which violates eigenstate thermalization hypothesis in Krylov subspace. Our prediction opens a new horizon in exploring exotic quantum many-body physics with t-J model, and shall also make a step towards simulating the high-Tc physics in neutral atom systems.

Clifford circuits Augmented Matrix Product States for fermion systems

Authors: Jiale Huang, Xiangjian Qian, Mingpu Qin

arXiv ID: 2501.00413 | Date: 2024-12-31

Abstract: Clifford circuits Augmented Matrix Product States (CAMPS) was recently proposed to leverage the advantages of both Clifford circuits and Matrix Product States (MPS). Clifford circuits can support large entanglement and can be efficiently simulated classically according to the Gottesman-Knill theorem. So in CAMPS, MPS needs only to handle the so-called Non-stabilizerness Entanglement Entropy which significantly improves the simulation accuracy for a given bond dimension. In this work, we generalize CAMPS to study the Fermion system by taking advantage of the Jordan-Wigner transformation which can map the studied Fermion system to a spin system. We benchmark the method on both the spinless tVt-V model and the spinful Hubbard model. Our test results show significant improvement of the accuracy of CAMPS over MPS, especially when the interactions are strong. Fermionic CAMPS provides a useful tool for the accurate study of many-body fermion systems in the future and has the potential to help resolve long-standing issues.

Programming guide for solving constraint satisfaction problems with tensor networks

Authors: Xuanzhao Gao, Xiaofeng Li, Jinguo Liu

arXiv ID: 2501.00227 | Date: 2024-12-31

Abstract: Constraint satisfaction problems (CSPs) are a class of problems that are ubiquitous in science and engineering. It features a collection of constraints specified over subsets of variables. A CSP can be solved either directly or by reducing it to other problems. This paper introduces the Julia ecosystem for solving and analyzing CSPs, focusing on the programming practices. We introduce some of the important CSPs and show how these problems are reduced to each other. We also show how to transform CSPs into tensor networks, how to optimize the tensor network contraction orders, and how to extract the solution space properties by contracting the tensor networks with generic element types. Examples are given, which include computing the entropy constant, analyzing the overlap gap property, and the reduction between CSPs.

Evidence for a Z2\mathbb{Z}_{2} Dirac spin liquid in the generalized Shastry-Sutherland model

Authors: Atanu Maity, Francesco Ferrari, Jong Yeon Lee, Janik Potten, Tobias Müller, Ronny Thomale, Rhine Samajdar, Yasir Iqbal

arXiv ID: 2501.00096 | Date: 2024-12-30

Abstract: We present a multimethod investigation into the nature of the recently reported quantum spin liquid (QSL) phase in the spin-1/21/2 Heisenberg antiferromagnet on the Shastry-Sutherland lattice. A comprehensive projective symmetry group classification of fermionic mean-field Ansätze on this lattice yields 46 U(1) and 80 Z2\mathbb{Z}_{2} states. Motivated by density-matrix renormalization group (DMRG) calculations suggesting that the Shastry-Sutherland model and the square-lattice J1J_{1}-J2J_{2} Heisenberg antiferromagnet putatively share the same QSL phase, we establish a mapping of our Ansätze to those of the square lattice. This enables us to identify the equivalent of the square-lattice QSL (Z2Azzzz13) in the Shastry-Sutherland system. Employing state-of-the-art variational Monte Carlo calculations with Gutzwiller-projected wavefunctions improved upon by Lanczos steps, we demonstrate the excellent agreement of energies and correlators between a gapless (Dirac) Z2\mathbb{Z}_{2} spin liquid -- characterized by only few parameters -- and approaches based on neural quantum states and DMRG. Furthermore, the real-space spin-spin correlations are shown to decay with the same power law as in the J1J_{1}-J2J_{2} square lattice model, which also hosts a Z2\mathbb{Z}_{2} Dirac spin liquid. Finally, we apply the recently developed Keldysh formulation of the pseudo-fermion functional renormalization group to compute the dynamical spin structure factor; these correlations exhibit the features expected due to Dirac cones in the excitation spectrum, thus providing strong independent evidence for a Dirac QSL ground state. Our finding of a dd-wave pairing Z2\mathbb{Z}_{2} Dirac QSL is consistent with the recently observed signatures of QSL behavior in Pr2_2Ga2_2BeO7_7 and outlines predictions for future experiments.

The surface code beyond Pauli channels: Logical noise coherence, information-theoretic measures, and errorfield-double phenomenology

Authors: Jan Behrends, Benjamin Béri

arXiv ID: 2412.21055 | Date: 2024-12-30

Abstract: We consider the surface code under errors featuring both coherent and incoherent components and study the coherence of the corresponding logical noise channel and how this impacts information-theoretic measures of code performance, namely coherent information and quantum relative entropy. Using numerical simulations and developing a phenomenological field theory, focusing on the most general single-qubit X-error channel, we show that, for any nonzero incoherent noise component, the coherence of the logical noise is exponentially suppressed with the code distance. We also find that the information-theoretic measures require this suppression to detect optimal thresholds for Pauli recovery; for this they thus require increasingly large distances for increasing error coherence and ultimately break down for fully coherent errors. To obtain our results, we develop a statistical mechanics mapping and a corresponding matrix-product-state algorithm for approximate syndrome sampling. These methods enable the large scale simulation of these non-Pauli errors, including their maximum-likelihood thresholds, away from the limits captured by previous approaches.